
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 \(a\) and \(b\) be angles such that \(\cos a + \cos b = \frac{3}{5}\) and \(\sin a + \sin b = \frac{1}{5}.\) Find
\[
\tan \left( \frac{a + b}{2} \right).
\]

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