
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
Two arithmetic progressions are given. The first and fifth terms of the first progression are 7 and -5, respectively. The first term of the second progression is 0, and the last term is $7 / 2$. Find the sum of the terms of the second progression, given that the third terms of both progressions are equal.

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