
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 \(\alpha, \beta, \gamma\) satisfy \(0<\alpha<\beta<\gamma<2 \pi\), and for any \(x \in \mathbf{R}\), \(\cos (x+\alpha) + \cos (x+\beta) + \cos (x+\gamma) = 0\), determine the value of \(\gamma - \alpha\).

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