
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 that \(\cos \alpha + \cos \beta + \cos \gamma = \sqrt{\frac{1}{5}}\) and \(\sin \alpha + \sin \beta + \sin \gamma = \sqrt{\frac{4}{5}}\), find \(\cos (\alpha - \beta) + \cos (\beta - \gamma) + \cos (\gamma - \alpha)\).

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