
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
Find the solution to the equation:

$$
\frac{1+\cos (2 \alpha-2 \pi)+\cos (4 \alpha+2 \pi)-\cos (6 \alpha-\pi)}{\cos (2 \pi-2 \alpha)+2 \cos ^{2}(2 \alpha+\pi)-1} = 2 \cos 2 \alpha
$$

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