
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
(1) Given a point $P(-4,3)$ on the terminal side of angle $\alpha$, find the value of $\dfrac{\cos(\frac{\pi}{2}+\alpha)\sin(-\pi-\alpha)}{\cos(\frac{11\pi}{2}-\alpha)\sin(\frac{9\pi}{2}+\alpha)}$.
(2) Given that $\cos(\pi+\alpha)=-\dfrac{1}{2}$ and $\alpha$ is an angle in the fourth quadrant, calculate $\dfrac{\sin{\left[\alpha+(2n+1)\pi\right]}+\sin{\left[\alpha-(2n+1)\pi\right]}}{\sin(\alpha+2n\pi)\cdot\cos(\alpha-2n\pi)}$ where $n\in Z$.

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