
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
According to exercise B. 4283, if a $23 \times 23$ square is decomposed into $1 \times 1$, $2 \times 2$, and $3 \times 3$ squares, then at least one $1 \times 1$ square is necessary. Where can the $1 \times 1$ square be located, given that exactly one appears in the decomposition?

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