
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 natural number  $n$  is called *nice* if it enjoys the following properties:
• The expression is made ​​up of  $4$  decimal digits;
• the first and third digits of  $n$  are equal;
• the second and fourth digits of  $n$  are equal;
• the product of the digits of  $n$  divides  $n^2$ .
Determine all nice numbers.

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