
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 the vertex of angle $\theta$ is at the origin, its initial side coincides with the positive x-axis, and the terminal side lies on the line $2x - y = 0$, calculate $\frac{\sin\left(\frac{3\pi}{2} + \theta\right) + \cos\left(\pi - \theta\right)}{\sin\left(\frac{\pi}{2} - \theta\right) - \sin\left(\pi - \theta\right)}$

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