
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
In $\triangle ABC$, $\sin \frac{\angle ABC}{2} = \frac{\sqrt{3}}{3}$, $AB = 2$, point $D$ is on line segment $AC$ such that $AD = 2DC$, and $BD = \frac{4\sqrt{3}}{3}$. Find:
(1) The length of $BC$;
(2) The area of $\triangle DBC$.

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