
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
In the cartesian coordinate system $(xOy)$, if the initial side of angle $\alpha$ is the non-negative half of the $x$-axis, and the terminal side is the ray $l$: $y=2x(x\leqslant 0)$.
(I) Find the value of $\tan 2\alpha$;
(II) Find the value of $\frac{2\cos ^{2} \frac{\alpha}{2}-2\sin (\alpha-\pi)-1}{\sqrt{2}\cos (\alpha-\frac{7\pi}{4})}$.

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