
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 $\sin(3\pi + \alpha) = 2\sin(\frac{3\pi}{2} + \alpha)$, find the value of $\frac{\sin{\alpha} - 4\cos{\alpha}}{5\sin{\alpha} + 2\cos{\alpha}}$.

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