
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 $\cos(15°+\alpha) = \frac{15}{17}$, with $\alpha \in (0°, 90°)$, find the value of $\sin(15°-\alpha)$.  
(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