
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 that $a$, $b$, $c$ are the opposite sides of angles $A$, $B$, $C$ in triangle $\triangle ABC$, if $\triangle ABC$ simultaneously satisfies three of the following four conditions:①$a=\sqrt{3}$; ②$b=2$; ③$\frac{{sinB+sinC}}{{sinA}}=\frac{{a+c}}{{b-c}}$; ④${cos^2}({\frac{{B-C}}{2}})-sinBsinC=\frac{1}{4}$.<br/>$(1)$ What are the possible combinations of conditions that have a solution for the triangle?<br/>$(2)$ Among the combinations in $(1)$, choose one and find the area of the corresponding $\triangle ABC$.

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