
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 checkers that can be placed on a $6 \times 6$ board such that no three checkers (specifically, the centers of the cells they occupy) are on the same line (regardless of the angle of inclination)?

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