
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
Solve the equation for \( x \):
$$
\left(\cos^2 \theta\right) x^3 - \left(1 + 3 \sin^2 \theta\right) x + \sin 2 \theta = 0.
$$

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