
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 the function $f(x) = \sin^2 x + \sin x \cos x$, when $x = \theta$, the function $y=f(x)$ attains its minimum value. Find the value of $\frac{\sin 2\theta + 2\cos \theta}{\sin 2\theta - 2\cos 2\theta}$.

A) $-3$
B) $3$
C) $-\frac{1}{3}$
D) $\frac{1}{3}$

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