
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
Given an arithmetic sequence $\{a_n\}$, the sum of its first $n$ terms is $S_n$. If $S_p = \frac{p}{q}$ and $S_q = \frac{q}{p}$ ($p \neq q$), determine the value of $S_{p+q}$.

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