
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 scalene triangle on a plane, Peter and Basil take turns performing the following operations: each round, Peter chooses a point on the plane, and Basil decides to color that point either red or blue. Peter wins if there exists a triangle similar to the original triangle with vertices all of the same color. Find the minimum number of rounds needed so that regardless of Basil's moves, Peter is guaranteed to win in a certain number of rounds (this value should be independent of the shape of the original triangle).

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