
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 trapezoid $ABCD$ with $AD||BC$, it's known that $BD = 2$, $\angle DBA = 30^{\circ}$, and $\angle BDC = 60^{\circ}$. The ratio $BC:AD$ is $7:3$. Determine the length of $CD$.
A) $\frac{4}{3}$
B) $\frac{5}{3}$
C) $\frac{8}{3}$
D) $\frac{11}{3}$

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