
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
a) Find a four-digit number that is a perfect square and such that its first two digits are identical and its last two digits are also identical.

b) A two-digit number, when summed with the number formed by reversing its digits, results in a perfect square. Find all such numbers.

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