
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
Considering the triple angle formulas for sine and cosine, $\sin 3\theta = 3 \sin \theta - 4 \sin^3 \theta$ and $\cos 3\theta = 4 \cos^3 \theta - 3 \cos \theta$, and the expressions $\frac{\cos 3\theta}{\cos \theta} = 4 \cos^2 \theta - 3$ and $\frac{\sin 3\theta}{\sin \theta} = 3 - 4 \sin^2 \theta$, what kind of trigonometric function problem can you construct?

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