
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 $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, with $B=60^{\circ}$ and $a^{2}=b^{2}+c^{2}-bc$. Extend $BC$ to $D$ such that $BD=7$, and the area of $\triangle ACD$ is $\frac{3}{2}\sqrt{3}$.<br/>$(Ⅰ)$ Find the length of $AB$;<br/>$(Ⅱ)$ Find the area of the circumcircle of $\triangle ACD$.

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