
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 drew a square on a plane, divided it into 64 equal smaller squares, and colored them in a checkerboard pattern with black and white colors. After that, Petya chose a point strictly inside one of these smaller squares. Vasya can draw any closed polyline on the plane without self-intersections and receive an answer to the question of whether the chosen point is strictly inside the polyline or not. What is the minimum number of such questions Vasya needs to ask to determine the color of the square containing the chosen point — white or black?

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