
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
Given vectors $\overrightarrow {a} = (\cos\alpha, \sin\alpha)$, $\overrightarrow {b} = (\cos\beta, \sin\beta)$, and $|\overrightarrow {a} - \overrightarrow {b}|=1$.  
(1) Find the value of $\cos(\alpha-\beta)$.  
(2) If $-\frac{\pi}{2} < \beta < 0 < \alpha < \frac{\pi}{2}$ and $\sin\beta = -\frac{1}{7}$, find the value of $\sin\alpha$.

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