
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 $s_1$ be the sum of the first $n$ terms of the arithmetic sequence $3, 10, \cdots$ and let $s_2$ be the sum of the first $n$ terms of the arithmetic sequence $5, 8, \cdots$. Determine the number of values of $n$ for which the equation $s_1 = s_2$ is true.

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