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

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