
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 $α \in \left(0, \frac{π}{2}\right)$, $β \in \left(\frac{π}{2}, π\right)$, $\cos β = -\frac{1}{3}$, and $\sin(α + β) = \frac{4 - \sqrt{2}}{6}$.

(1) Find the value of $\tan 2β$;

(2) Find the value of $α$.

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