
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
Given a triangle with no equal angles, Petya and Vasya play the following game: in one move, Petya marks a point on the plane, and Vasya colors it in either red or blue. Petya wins if any three of the points he has marked and Vasya has colored form a monochromatic triangle similar to the original one. What is the minimum number of moves Petya must make to guarantee his win (regardless of the original triangle)?

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