
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
Pete and Vasya received identical sets of $N$ weights, where the masses of any two weights differ by no more than 1.25 times. Pete managed to divide all the weights in his set into 10 groups of equal mass, while Vasya managed to divide all the weights in his set into 11 groups of equal mass. Find the smallest possible value of $N$.

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