
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
The decimal representation of the natural number \( a \) consists of \( n \) identical digits \( x \), the number \( b \) consists of \( n \) identical digits \( y \), and the number \( c \) consists of \( 2n \) identical digits \( z \). For any \( n \geq 2 \), find all such digits \( x, y, z \) for which \( a^2 + b = c \).

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