
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
Petya and Vasya are given equal sets of  $ N$  weights, in which the masses of any two weights are in ratio at most  $ 1.25$ . Petya succeeded to divide his set into  $ 10$  groups of equal masses, while Vasya succeeded to divide his set into  $ 11$  groups of equal masses. Find the smallest possible  $ N$ .

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