
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
Let $\theta \in \left(0, \frac{\pi}{2}\right)$, and $\cos\left(\theta + \frac{\pi}{6}\right) = \frac{1}{3}$.  
(1) Find the value of $\sin\theta$;  
(2) Find the value of $\sin\left(2\theta + \frac{\pi}{6}\right)$.

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