
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 four digit number is called *stutterer* if its first two digits are the same and its last two digits are also the same, e.g.  $3311$  and  $2222$  are stutterer numbers. Find all stutterer numbers that are square numbers.

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