
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 $\triangle ABC$, let $a$, $b$, $c$ be the lengths of the sides opposite angles $A$, $B$, and $C$ respectively, and $\left(c-b\right)\sin C=\left(a-b\right)\left(\sin A+\sin B\right)$.<br/>$(1)$ Find the value of angle $A$;<br/>$(2)$ If $b=2$ and $\triangle ABC$ is an acute triangle, find the range of the area $S$ of $\triangle ABC$.

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