
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system

The pensioners on one of the planets of Alpha Centauri enjoy spending their free time solving numeric puzzles: they choose natural numbers from a given range $[A, B]$ such that the sum of any two chosen numbers is not divisible by a certain number $N$. Last week, the newspaper "Alpha Centaurian Panorama" offered its readers a puzzle with the values $A=1353$, $B=2134$, and $N=11$. What is the maximum number of numbers that can be the solution to such a puzzle?

Present the answer in LaTex format: \boxed{Your answer}
user