
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 \( 0 \leqslant \alpha \leqslant \beta < \gamma \leqslant 2\pi \) and \(\cos \alpha + \cos \beta + \cos \gamma = 0\) and \(\sin \alpha + \sin \beta + \sin \gamma = 0\), calculate the value of \(\beta - \alpha\).

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