
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 $\sin \alpha= \frac{3}{5}, \cos \beta= \frac{4}{5}$, where $\alpha \in \left( \frac{\pi}{2},\pi \right), \beta \in \left(0, \frac{\pi}{2} \right)$, find $\cos (\alpha+\beta)$; (2) Given $\cos \alpha= \frac{1}{7}, \cos (\alpha-\beta)= \frac{13}{14}$, and $0 < \beta < \alpha < \frac{\pi}{2}$, find the value of $\beta$.

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