
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 $\tan(\pi + \alpha) = -\frac{1}{2}$, find the value of the following expressions:

(1) $\frac{2\cos(\pi - \alpha) - 3\sin(\pi + \alpha)}{4\cos(\alpha - 2\pi) + \sin(4\pi - \alpha)}$;

(2) $\sin(\alpha - 7\pi)\cos(\alpha + 5\pi)$.

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