
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
In decimal form, 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 $n \geqslant 2$, find all numbers $x, y, z$ that satisfy $a^{2} + b = c$.

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