“A journey of a thousand miles begins with a single step.”

Lao Tzu, Chinese philosopher

Or if you’re the Boston Red Sox, you’re hoping it began with a sweep of the Kansas City Royals over the weekend. The Red Sox came out of the All-Star break in last place, 91/2 games back in the division. Winning the first three games after the break cut two games off that gap and brought them within six games of a wild-card spot.

It’s still a significant hole, but comeback victories Friday and Saturday, and a 6-0 victory Sunday kept the small flame of hope flickering at Fenway.

Now Boston must rise to a more formidable task. Beginning with Monday night’s game at Toronto, the Sox play 13 consecutive games against AL East opponents. Every game is a two-game swing against one of the teams they’re trying to catch.

The non-waiver trade deadline falls in the middle of that stretch, meaning what the Sox do now will determine how General Manager Ben Cherington handles his business in the hours and days before that deadline.

Everyone in the Red Sox clubhouse knows these games are more important because of the team’s poor start. There’s no hiding it.

“Given where we are right now, yes,” said Manager John Farrell. “That’s not to add any pressure. That’s to say that there’s some additional significance to the games when you play the teams ahead of you.”

A week ago, as the game’s stars gathered in Minnesota, it was hard to imagine there’d be any significance to the final 67 games of the season. Yet the momentum built by winning 4 of 5 before the break was continued against the Royals.

Now the Sox have to prove they can take that on the road against teams competing for playoff position.

The offense, moribund for most of the first half, has shown signs of life with contributions from young players and veterans alike.

Catcher Christian Vazquez has had an immediate impact, both behind the plate and in the batter’s box. Brock Holt continues to lead the way at the top of the order and Jackie Bradley Jr. has had his best month of the season.

Added to that has been clutch hitting from some of the players who led the way in 2013. Johnny Gomes hit a pinch-hit, two-out, two-run homer Friday night to give the Sox their first lead of the game. Mike Napoli hit a massive home run Saturday and scored both runs in a 2-1 victory.

Through it all, the Sox continue to pitch. Clay Buchholz is 3-1, 3.28 since coming back from the disabled list. Rubby De La Rosa is 3-0, 1.38 at Fenway Park this season. Jon Lester is 4-0, 0.85 in his last seven starts.

And the bullpen continues to improve, with Junichi Tazawa and Andrew Miller providing righty and lefty options for Farrell to get to closer Koji Uehara.

All of this sounds like a team competing for first place, not last. And if this were opening day, we’d make the argument that the Sox are ready to compete in the flawed AL East.

The Sox will play their 100th game Tuesday night in Toronto. There’s still a lot of baseball left but not a lot of time to overcome the self-induced trouble they find themselves in.

Winning 90 games might just be the baseball equivalent of a 1,000-mile journey. With the first small steps behind them, the Sox know they can’t afford to stumble as the voyage continues.

Tom Caron is the studio host for Red Sox broadcasts on NESN. His column appears in the Press Herald on Tuesdays.