
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 number $\overline{xyz}$ is a three-digit number written in the base-10 numeral system, and its square is a five-digit number: $\overline{xyz^{2}}=\overline{abcde}$ and $\overline{zyx^{2}}=\overline{edcba}$. How many such three-digit numbers exist and which ones are they?

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