
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 $\tan \alpha = 2$, find the value of the following expressions:
$$(1) \frac{\sin \alpha - 4 \cos \alpha}{5 \sin \alpha + 2 \cos \alpha};$$
$$(2) 4\sin^{2}{\alpha} - 3\sin{\alpha}\cos{\alpha} - 5\cos^{2}{\alpha}.$$

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