
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
Let's call the distance between numbers the absolute value of their difference. It is known that the sum of the distances from twenty consecutive natural numbers to some number \( a \) is 4460, and the sum of the distances from these same twenty numbers to the number \( a^2 \) is 2755. Find all possible values of \( a \).

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