
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: $\tan \alpha = -2$, find the value of:

$(1)$ $\frac{\sin \alpha + 5\cos \alpha}{-2\cos \alpha + \sin \alpha}$.

$(2)$ The value of $\sin \left(\alpha - 5\pi\right)\sin \left( \frac{3\pi}{2} - \alpha\right)$.

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