
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
In triangle $\triangle ABC$, it is known that $\cos B - \cos \frac{{A+C}}{2} = 0$.  
$(1)$ Find the measure of angle $B$.  
$(2)$ Let the sides opposite angles $A$, $B$, and $C$ be $a$, $b$, and $c$, respectively. If $8a = 3c$ and the altitude from $AC$ is $\frac{{12\sqrt{3}}}{7}$, find the perimeter of $\triangle ABC$.

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