
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
Several cells of a \(14 \times 14\) board are marked. It is known that no two marked cells lie in the same row or the same column, and that a knight can start from one of the marked cells and visit all the marked cells exactly once by making several jumps. What is the maximum possible number of marked cells?

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