
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 $\alpha, \beta \in \left(0, \frac{\pi}{2}\right)$ and $\sin(\alpha + 2\beta) = \frac{1}{3}$,

(3) If $\alpha + \beta = \frac{2\pi}{3}$, find the value of $\sin\beta$;

(4) If $\sin\beta = \frac{4}{5}$, find the value of $\cos\alpha$.

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