
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 identical smaller squares, and colored them in a checkerboard pattern in black and white. After that, he chose a point located strictly inside one of these smaller squares. Vasya can draw any closed polygonal line without self-intersections on the plane and get an answer to the question of whether the chosen point is strictly inside the polygonal line or not. What is the minimum number of such questions that Vasya needs to ask to determine the color of the chosen point - black or white?

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