
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
(1) Given $f(x) = \sqrt{\frac{1-x}{1+x}}$, and $\alpha \in \left(\frac{\pi}{2}, \pi\right)$, find $f(\cos\alpha) + f(-\cos\alpha)$;  
(2) Evaluate $\sin 50^\circ(1 + \sqrt{3}\tan 10^\circ)$.

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