
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 two-digit number $\overline{ab}$, written in the decimal system, when squared results in a three-digit number: $\overline{ab^{2}} = \overline{cde}$.

Reversing the digits of the original two-digit number and then squaring it also results in a three-digit number, and this latter squared number, when its digits are reversed, yields the previous squared number: $\overline{ba^{2}} = \overline{edc}$.

How many such two-digit numbers exist and what are they?

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