
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
Choose one of the three conditions from the following:①$c^{2}+ab=c\left(a\cos B-b\cos A\right)+2b^{2}$, ②$\left(b+c\right)\cdot \left(\sin B-\sin C\right)=-a\left(\sin A-\sin B\right)$, ③$bsinC=\sqrt{3}({a-c•cosB})$, and supplement the blank in the question below, then solve the following:<br/>Let the sides opposite angles $A$, $B$, and $C$ in $\triangle ABC$ be $a$, $b$, and $c$, respectively. Given _____.<br/>$(1)$ Find the measure of angle $C$;<br/>$(2)$ If $c=2\sqrt{3}$, find the range of values for $4\sin B-a$.<br/>Note: If multiple conditions are chosen and solved separately, the scoring will be based on the first answer.

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