
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) Simplify: $\dfrac{\tan(3\pi-\alpha)\cos(2\pi-\alpha)\sin(-\alpha+\dfrac{3\pi}{2})}{\cos(-\alpha-\pi)\sin(-\pi+\alpha)\cos(\alpha+\dfrac{5\pi}{2})}$;

(2) Given $\tan\alpha=\dfrac{1}{4}$, find the value of $\dfrac{1}{2\cos^{2}\alpha-3\sin\alpha\cos\alpha}$.

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