
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
Write an even number of ones in a row. Subtract from this number a number composed of a series of twos, half as long as the first series of ones. You will get a perfect square. (For example, \(1111 - 22 = 1089 = 33^2\)). Could you explain why?

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