
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 $\tan \theta = -\frac{3}{4}$, find the value of the following expressions:

$(1) \frac{\sin \left( \theta + \frac{3\pi }{2} \right)+\cos \left( \theta -\frac{\pi }{2} \right)}{2\sin \left( \pi +\theta \right)+\cos \left( \theta -\pi \right)}$

$(2) \sin \theta \cos \theta - \cos^2 \theta$

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