
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 $\overrightarrow{a}=(\sin \alpha,\cos \alpha)$, $\overrightarrow{b}=(1, \sqrt {3})$, $\alpha\in\left( \frac {\pi}{2},\pi\right)$, if $\overrightarrow{a}\perp \overrightarrow{b}$,  
$(1)$ find the value of $\alpha$;  
$(2)$ if $\sin (\alpha-\beta)= \frac {3}{5},\beta\in\left( \frac {\pi}{6}, \frac {\pi}{2}\right)$, find the magnitude of angle $\beta$.

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