
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 that $2\sin\alpha = \cos\alpha$.
1. If $\alpha$ is in the third quadrant, find the value of $\cos(x - \alpha)$.
2. Find the value of $$\frac{1 + 2\sin\alpha\sin(\frac{\pi}{2} - \alpha)}{\sin^2\alpha - \cos^2\alpha}$$.

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