
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
A *triminó* is a rectangular tile of  $1\times 3$ . Is it possible to cover a  $8\times8$  chessboard using  $21$  triminós, in such a way there remains exactly one  $1\times 1$  square without covering? In case the answer is in the affirmative, determine all the possible locations of such a unit square in the chessboard.

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