
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
Squares of integers that are palindromes (i.e., they read the same left-to-right and right-to-left) are an interesting subject of study. For example, the squares of $1, 11, 111,$ and $1111$ are $1, 121, 12321,$ and $1234321$ respectively, and all these numbers are palindromes. This rule applies to any number of ones up to 9. However, there are irregular cases, such as $264^2 = 69696$ and $2285^2 = 5221225$. 

In all the above examples, the number of digits is odd. Could the reader provide examples with an even number of digits?

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