
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 $p$ and $q$ be angles such that $\cos p + \cos q = \frac{3}{5}$ and $\sin p + \sin q = \frac{1}{4}.$ Find $\tan \left( \frac{p + q}{2} \right).$

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