
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
Let $\triangle ABC$ have sides $a$, $b$, $c$ opposite to angles $A$, $B$, $C$ respectively. Given $\sqrt{3}acos\frac{{A+C}}{2}=bsinA$. Find:<br/>
$(1)$ $B$;<br/>
$(2)$ If $\triangle ABC$ is an acute triangle, find the range of $\frac{{a+b}}{c}$.

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