
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
The sum of the absolute values of the terms of a finite arithmetic progression is 100. If all its terms are increased by 1 or all its terms are increased by 2, the sum of the absolute values of the terms of the resulting progression will also be 100. What values can the quantity $n^{2} d$ take under these conditions, where $d$ is the common difference of the progression and $n$ is the number of its terms?

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