
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 first term of an arithmetic sequence is $a_{1}$, and the sum of its first and $n$-th term is $s_{a}$. Another arithmetic sequence has the corresponding data $b_{1}$ and $s_{b}$. A third sequence is formed in such a way that the term of arbitrary position is equal to the product of the terms of the same position from the first two sequences. What is the sum of the first $n$ terms of the third sequence?

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