
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
Trapezoid $ABCD$ has $AD \parallel BC$, $BD = 2$, $\angle DBA = 30^\circ$, and $\angle BDC = 60^\circ$. The ratio $BC: AD$ is $7: 3$. Determine the length of $CD$.
A) $\frac{5}{3}$
B) $\frac{14}{3}$
C) $\frac{8}{3}$
D) $\frac{9}{3}$
E) $\frac{11}{3}$

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