
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
Given $\cos \alpha = \tan \beta$, $\cos \beta = \tan \gamma$, $\cos \gamma = \tan \alpha$, find that $\sin^2 \alpha = \sin^2 \beta = \sin^2 \gamma = \cos^4 \alpha = \cos^4 \beta = \cos^4 \gamma = 4 \sin^2 18^\circ$.

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