
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 angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given that $\left(\sin A+\sin B\right)\left(a-b\right)=c\left(\sin C-\sin B\right)$, and $D$ is a point on side $BC$ such that $AD$ bisects angle $BAC$ and $AD=2$. Find:<br/>
$(1)$ The measure of angle $A$;<br/>
$(2)$ The minimum value of the area of triangle $\triangle ABC$.

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