
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 square chalkboard divided into squares of equal size, with one diagonal drawn in each square, find the smallest number of total squares that satisfies the condition that the total number of smaller squares along the perimeter of the chalkboard is twice the number of them along one of its diagonals.

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