
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 $\triangle ABC$, $a=2\sqrt{3}$, $a^{2}+c^{2}-\sqrt{3}ac=b^{2}$.<br/>$(Ⅰ)$ Find $\angle B$;<br/>$(Ⅱ)$ Choose one of the following conditions as known to ensure the existence and uniqueness of $\triangle ABC$, and find the area of $\triangle ABC$.<br/>Condition 1: $b=3$;<br/>Condition 2: $\cos A=\frac{4}{5}$;<br/>Condition 3: The perimeter of $\triangle ABC$ is $4+2\sqrt{3}$.

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