
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

$$
\cos \left(\frac{5}{2} \pi-6 \alpha\right) \cdot \sin ^{3}(\pi-2 \alpha)-\cos (6 \alpha-\pi) \cdot \sin ^{3}\left(\frac{\pi}{2}-2 \alpha\right)=\cos ^{3} 4 \alpha
$$

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