
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
Find all  $10$ -digit whole numbers  $N$ , such that first  $10$  digits of  $N^2$  coincide with the digits of  $N$  (in the same order).

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