
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 $\sin \alpha =\frac{3}{5}$ and $\cos \beta =\frac{4}{5}$, where $\alpha \in \left(\frac{\pi }{2},\pi \right)$ and $\beta \in \left(0,\frac{\pi }{2}\right)$, find $\cos (\alpha +\beta )$.

(2) Given $\cos \alpha =\frac{1}{7}$ and $\cos (\alpha -\beta )=\frac{13}{14}$, with $0 < \beta < \alpha < \frac{\pi }{2}$, find the value of $\beta$.

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