
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 that $α, β ∈ (0, \frac{π}{2})$, 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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