
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 $\cos \alpha =\frac{\sqrt{5}}{3}, \alpha \in \left(-\frac{\pi }{2},0\right)$, find $\sin (\pi -\alpha)$;

(2) Given $\cos \left(\theta+ \frac{\pi}{4}\right)= \frac{4}{5}, \theta \in \left(0, \frac{\pi}{2}\right)$, find $\cos \left(\frac{\pi }{4}-\theta \right)$.

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