
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 $$\alpha \in (0, \frac{\pi}{2})$$ and $$\beta \in (\frac{\pi}{2}, \pi)$$, with $$\cos\beta = -\frac{1}{3}$$ and $$\sin(\alpha + \beta) = \frac{4 - \sqrt{2}}{6}$$.
- (I) Find the value of $\tan 2\beta$;
- (II) Find the value of $\alpha$.

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