
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 quadrilateral $ABCD$ on the plane, $\angle ABC=\dfrac{\pi }{3}$, $\angle ADC=\dfrac{\pi }{2}$, and $BC=2$.
1. If the area of $\triangle ABC$ is $\dfrac{3\sqrt {3}}{2}$, find $AC$.
2. If $AD=2\sqrt {3}$, $\angle ACB=\angle ACD+\dfrac{\pi }{3}$, find $\tan \angle ACD$.

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