
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
Do there exist three distinct digits \( A, B, C \) such that \(\overline{ABC}\), \(\overline{CBA}\), and \(\overline{CAB}\) are squares of natural numbers? (The bar over the digits indicates the number formed by these digits in the specified order.)

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