
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
Consider an arithmetic progression made up of  $100$  terms. If the sum of all the terms of the progression is  $150$  and the sum of the even terms is  $50$ , find the sum of the squares of the  $100$  terms of the progression.

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