
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 $0 < \alpha < \pi$, $\tan\alpha = -2$.
(1) Find the value of $\sin\left(\alpha + \frac{\pi}{6}\right)$;
(2) Calculate the value of $$\frac{2\cos\left(\frac{\pi}{2} + \alpha\right) - \cos(\pi - \alpha)}{\sin\left(\frac{\pi}{2} - \alpha\right) - 3\sin(\pi + \alpha)};$$
(3) Simplify $2\sin^2\alpha - \sin\alpha\cos\alpha + \cos^2\alpha$.

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