
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 marks four points on the plane so that they cannot all be crossed out by two parallel lines. From the lines passing through pairs of points, Vasya chooses two, measures the angle between them, and pays Petya an amount equal to the measure of the angle in degrees. What is the maximum amount Petya can guarantee himself?

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