
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 \(\alpha\), \(\beta\), and \(\gamma\) satisfy \(0 < \alpha < \beta < \gamma < 2\pi\). If \(\cos (x+\alpha)+\cos (x+\beta)+\cos (x+\gamma)=0\) holds for any real number \(x\), find the value of \(\alpha-\beta\).

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