
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=-\frac{4}{3} $, find:

(1) $\sin \alpha+\cos \alpha $

(2) $\frac{\sin (π-\alpha)+2\cos \left(π+\alpha\right)}{\sin ( \frac{3}{2}π-\alpha)-\cos ( \frac{3π}{2}+\alpha)}$.

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