
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 opposite sides of angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively. Given that $\left(a-b\right)\left(\sin A+\sin B\right)=c\left(\sin A-\sin C\right)$, $b=2$, and $a=\frac{{2\sqrt{6}}}{3}$. Find:<br/>
$(1)$ The diameter of the circumcircle of triangle $\triangle ABC$;<br/>
$(2)$ The area of triangle $\triangle ABC$.

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