
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
This question is worth a total of 10 points.

(1) Given $\cos \alpha = -\frac{4}{5}$, and $\alpha$ is an angle in the third quadrant. Find the value of $\sin \alpha$;  
(2) Given $\tan \theta = 3$, find the value of $\frac{\sin \theta + \cos \theta}{2\sin \theta + \cos \theta}$.

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