
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
There exists a class of numbers such that both the number and its reversed form are three-digit numbers and perfect squares. How many such numbers exist?

Note: The normal order of a number is read from left to right, and the reverse order is read from right to left. For example, the three-digit number 123 has an order of 123 and a reverse order of 321.
A perfect square can be expressed in the form of $a \times a$. For example, $121 = 11 \times 11$, so 121 is a perfect square.

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