When Chiefs coach Andy Reid joined the NFL’s exclusive 300-win club with his team’s 23-14 victory over the Houston Texans in the AFC Divisional Round, he promptly heard from the only living member of that Mt. Rushmore of coaching — Bill Belichick, both his longtime friend and rival.

Reid either didn’t immediately remember or quite want to share what Belichick had to say. But when I asked him Thursday if it was along the lines of “welcome to 300,” Reid laughed and invoked his own weight in the image of the “forktarian” he likes to call himself.

Belichick is “never going to really reach the real 300,” he said, meaning pounds. “There’s a lot of cheeseburgers that went into that.”

And so it goes with Reid, who loves self-deprecating humor any time but especially when he can use it to deflect or downplay the spotlight.

When he was asked earlier in the same interview session about having such success in his 60s, for instance, he said, “I think they put something in the Geritol.”

And asked what it would mean to him to win The Associated Press coach of the year award — as he deservedly should — Reid suggested he wasn’t aware he was in contention and added, “You could’ve just made that up.”

But there’s something more to all this than just the laughs and the humility of a man who always credits everyone around him for his achievements.

While Reid is competitive down to his marrow and every … single … cell, in ways that his nuanced public persona may not always show, a key reason for his incredible success isn’t that he is directly concentrating on winning an unprecedented three straight Super Bowls.

Or centered on becoming the winningest coach in NFL history (his 302 victories are 46 away from breaking Don Shula’s record).

Or even preoccupied with the idea of beating the Eagles in Super Bowl LIX for an encore Super Bowl victory over the franchise that let him go after the 2012 season.

“He is one of the best I ever faced,” Belichick, now the coach at North Carolina, said in an email to The Star. “This run is one of the best and longest in NFL history. Andy’s accomplishments are extraordinary.”

Even if such feats may occasionally flicker through Reid’s mind, they certainly don’t occupy it.

As far he’s concerned, that would be like blinding himself by looking directly into the sun.

Or paralyzing himself by looking back or forward too far.

Plus, Reid somehow is both intrinsically driven to give his all and consumed with the so-called precious present.

As sure as his offensive genius and ability to connect with players of every background, this is another of Reid’s superpowers … even if it’s not exactly a glamorous point.

Accordingly, I’m not sure he’s ever even uttered the term “three-peat.”

If so, Patrick Mahomes said Thursday, it would only be because he was asked about it by the media.

“He’s very locked in on just, ‘How can we be great with our cadence today at practice?’” Mahomes said.

Evidently referring not to the pace of the session but signal-calling sync, Mahomes added, “So that’s just the stuff that Coach Reid focuses on.”

Speaking of “focus,” it might seem like a dry cliche to say that Reid is virtually always engaged more in process than results.

And not on the destination as much as the journey. And treating every day with the same urgency — as anyone around him much will say he does.

Or that it’s all about “The Formula,” the last words the Chiefs see on their way from the GEHA Field at Arrowhead Stadium locker room to the field.

But the point is more amplified and colorful when you think of it through the lens of this time-honored Vince Lombardi quote:

“I firmly believe that any man’s finest hour, the greatest fulfillment of all that he holds dear, is that moment when he has worked his heart out in a good cause and lies exhausted on the field of battle — victorious.”

“Victorious” is the key term, because that’s the very reason to strive.

But I believe Reid also sees the work itself as a matter of virtue being its own reward.

That notion is reflected in another of my favorite quotes, written by University of Nebraska philosophy professor Hartley Burr Alexander and etched into Memorial Stadium in Lincoln, Nebraska:

“Not the victory but the action; not the goal but the game; in the deed the glory.”

Even if that sounds lofty, I really think it’s true when it comes to Reid.

For a snapshot of his thinking, let’s to back to training camp at Missouri Western in St. Joseph, where Reid believes the spartan conditions are essential to forming the foundation.

When he referred to the “cinder blocks” of the dorm rooms, he might as well have been speaking about the pillars of, well, the formula.

“Listen, there is a certain toughness this game requires …” Reid said there in July, later adding, “We’ve got that part of it going, and it’s important that you develop that.

“If you are fatigued, then you are going to be fatigued mentally. If you are fatigued physically, that’s going to affect you mentally. And if you are fatigued, period, then you can’t think and you can’t play. At least not to the best of your ability.

“So the objective here is let’s get ourselves in shape, make sure we are in football shape … both mentally and physically, so that we can perform at our best.”

That’s forever reinforced by his own example. Even within a profession of workaholics, Reid’s work ethic is legendary.

Because he burns to win, to be sure.

But also because he embraces every step it takes.

When I asked him if he finds the journey to be the most fulfilling part, Reid seemed to agree with the suggestion and said he thinks of himself first as a teacher.

“There is a lot that goes into that,” he said. “It’s not just knowing your stuff, but how it’s presented and the trust that you have in the guys and then the work that goes into each play.”

He added, “When we see success, we enjoy that; I enjoy that. I enjoy seeing the guys go out and do something good. I’m happy for them, because I know the time and the effort that went into it.

“There’s an aptitude part of that, you know?”

He meant in the learning.

But the aptitude, not to mention attitude, starts with the teaching and tone set by a one-of-a-kind force.

In those deeds, the glory — no matter how much he might try to laugh you off that.