
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  $a$  be number of  $n$  digits ( $ n > 1$ ). A number  $b$  of   $2n$  digits is obtained by writing two copies of  $a$  one after the other. If  $\frac{b}{a^2}$  is an integer  $k$ , find the possible values values of  $k$ .

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