
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 following two conditions to fill in the blank below and complete the question:<br/>①$b=acosC+\frac{1}{2}c$;<br/>②$si{n}^{2}A-(sinB-sinC)^{2}=2sinBsin(C+\frac{π}{3})-\sqrt{3}sinBcosC$.<br/>In $\triangle ABC$, where the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, if ____.<br/>$(1)$ Find $A$;<br/>$(2)$ If $bcosC+ccosB=\sqrt{7}$ and $b=2$, find $c$.

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