
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 that $\sin(\theta + 3\pi) = -\frac{2}{3}$, find the value of $\frac{\tan(-5\pi - \theta) \cdot \cos(\theta - 2\pi) \cdot \sin(-3\pi - \theta)}{\tan(\frac{7\pi}{2} + \theta) \cdot \sin(-4\pi + \theta) \cdot \cot(-\theta - \frac{\pi}{2})} + 2 \tan(6\pi - \theta) \cdot \cos(-\pi + \theta)$.

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