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

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