
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 $\tan (\frac{\pi}{4}+\alpha) = \frac{1}{2}$,
(I) Find the value of $\tan \alpha$;
(II) Find the value of $\frac{\sin (2\alpha+2\pi) - \sin^{2}(\frac{\pi}{2}-\alpha)}{1-\cos (\pi-2\alpha)+\sin^{2}\alpha}$.

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