
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
Vasya cut a triangle out of cardboard and numbered its vertices with the digits 1, 2, and 3. It turned out that if Vasya rotates his triangle clockwise around its vertex numbered 1 by an angle equal to the angle at this vertex 15 times, the triangle returns to its original position. If Vasya rotates the triangle clockwise around its vertex numbered 2 by an angle equal to the angle at this vertex 6 times, the triangle again returns to its original position. Vasya claims that if he rotates his triangle around the vertex numbered 3 by an angle equal to the angle at this vertex \( n \) times, the triangle will return to its original position. What is the minimum \( n \) that Vasya might have named such that his statement is true for at least some cardboard triangle?

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