
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
For integers \( a_{1}, \ldots, a_{n} \in\{1,2,3, \ldots, 9\} \), we use the notation \( \overline{a_{1} a_{2} \ldots a_{n}} \) to denote the number \( 10^{n-1} a_{1} + 10^{n-2} a_{2} + \cdots + 10 a_{n-1} + a_{n} \). For example, when \( a = 2 \) and \( b = 0 \), \( \overline{ab} \) denotes the number 20. Given that \( \overline{ab} = b^{2} \) and \( \overline{acbc} = (\overline{ba})^{2} \), find the value of \( \overline{abc} \).

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