
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
Fix an integer  $n \ge 2$ . A fairy chess piece *leopard* may move one cell up, or one cell to the right, or one cell diagonally down-left. A leopard is placed onto some cell of a  $3n \times 3n$  chequer board. The leopard makes several moves, never visiting a cell twice, and comes back to the starting cell. Determine the largest possible number of moves the leopard could have made. 

Dmitry Khramtsov, Russia

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