
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 value of the expression:

\[ \frac{\sin (2 \alpha + 2 \pi) + 2 \sin (4 \alpha - \pi) + \sin (6 \alpha + 4 \pi)}{\cos (6 \pi - 2 \alpha) + 2 \cos (4 \alpha - \pi) + \cos (6 \alpha - 4 \pi)}. \]

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