
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
Given that in triangle $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and $b^{2}+c^{2}-a^{2}=bc$. Find:<br/>
$(1)$ Angle $A$;<br/>
$(2)$ If the area of $\triangle ABC$ is $\frac{3\sqrt{3}}{2}$, and _____, find $a$.<br/>
(Choose one of the following conditions to complete the solution:① $\sin C+\sqrt{3}\cos C=2$; ② $b-c=\frac{\sqrt{3}}{3}a$.)

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