
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 $\alpha, \beta, \gamma$ satisfy $0 < \alpha < \beta < \gamma < 2\pi$. If for any $x \in \mathbf{R}$, $\cos(x + \alpha) + \cos(x + \beta) + \cos(x + \gamma) = 0$, then $\gamma - \alpha = \quad$ .

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