
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
\[\frac{\cos \left(4 \alpha - \frac{9}{2} \pi \right)}{\operatorname{ctg} \left( \frac{5}{4} \pi + 2 \alpha \right) \left( 1 - \cos \left( \frac{5}{2} \pi + 4 \alpha \right) \right)} = \operatorname{tg} 4 \alpha\]


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