
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 $\dfrac{\tan \alpha}{\tan \alpha - 1} = -1$, find the values of the following expressions:
1. $\dfrac{\sin \alpha - 3 \cos \alpha}{\sin \alpha + \cos \alpha}$
2. If $\alpha$ is an angle in the third quadrant, find $\cos (-\pi + \alpha) + \cos (\dfrac{\pi}{2} + \alpha)$.

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