
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
There is a chessboard with the usual coloring (the borders of the squares are considered to be colored in black).

Draw the circle with the largest radius that lies entirely on the black squares.

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