
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 triangle $\triangle ABC$ with angles $A$, $B$, and $C$, and sides $a$, $b$, and $c$ opposite to the angles, respectively. It is known that $\left(a+b+c\right)\left(b+c-a\right)=3bc$. Find:

$(Ⅰ)$ Angle $A$;

$(Ⅱ)$ If $a=2$ and the area of $\triangle ABC$ is $\sqrt{3}$, find the values of $b$ and $c$.

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