
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
What is the maximum number of 2 by 2 squares that can be placed on a 7 by 7 checkerboard so that any two placed squares share at most one common cell? The 2 by 2 squares are placed along the grid lines so that each covers exactly 4 cells. The squares do not go beyond the boundary of the board.

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