
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
Let  $ABCD$  be a square, such that the length of its sides are integers. This square is divided in  $89$  smaller squares,  $88$  squares that have sides with length  $1$ , and  $1$  square that has sides with length  $n$ , where  $n$  is an integer larger than  $1$ . Find all possible lengths for the sides of  $ABCD$ .

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