
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 an acute triangle $\triangle ABC$ with interior angles $A$, $B$, $C$ and corresponding sides $a$, $b$, $c$, where $\frac{{2a-c}}{{\cos({A+B})}}=\frac{b}{{\cos({A+C})}}$. Find:<br/>
$(1)$ The measure of angle $B$;<br/>
$(2)$ If $b=3$, find the range of values for $a+c$.

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