
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 $\triangle ABC$, it is known that the bisector of $\angle ABC$ intersects $AC$ at point $D$, and $BA = 2BC$.
(1) Find the ratio of the areas of $\triangle BDC$ and $\triangle BDA$;
(2) If $\angle ABC = 120^\circ$, $BC = 3$, find $AD$ and $DC$.

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