
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 that the terminal side of angle $\alpha$ passes through the point $P(-4,3)$, find the value of $\frac{\cos (\frac{\pi }{2}+\alpha )\sin (-\pi -\alpha )}{\cos (\frac{2019\pi }{2}-\alpha )\tan (\frac{9\pi }{2}+\alpha )}$.

(2) If $\tan (\frac{\pi }{4}+x)=2018$, find the value of $\frac{1}{\cos 2x}+\tan 2x$.

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