
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 $α,β∈(0, \frac {π}{2})$ and $\frac {\sin β}{\sin α}=\cos (α+β)$,  
$(1)$ If $α= \frac {π}{6}$, then $\tan β=$ _______ ;  
$(2)$ The maximum value of $\tan β$ is _______ .

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