
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
Twenty-one rectangles of size  $3\times 1$  are placed on an  $8\times 8$  chessboard, leaving only one free unit square. What position can the free square lie at?

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