
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
\(1-\cos (2 \alpha - \pi) + \cos (4 \alpha - 2 \pi) = 4 \cos 2 \alpha \cos \left(\frac{\pi}{6} + \alpha\right) \cos \left(\frac{\pi}{6} - \alpha\right)\).

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