
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
If \(\cot \alpha + \cot \beta + \cot \gamma = -\frac{4}{5}\), \(\tan \alpha + \tan \beta + \tan \gamma = \frac{17}{6}\) and \(\cot \alpha \cot \beta + \cot \beta \cot \gamma + \cot \gamma \cot \alpha = -\frac{17}{5}\), find the value of \(\tan (\alpha + \beta + \gamma)\).

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