
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 $14 \times 14$ chessboard are marked. It is known that no two of the marked cells are in the same row or column, and that a knight can travel from any marked cell to any other marked cell using only the marked cells. What is the maximum possible number of marked cells?

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