
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 $\triangle ABC$, $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$ respectively. Given $\overset{ -}{m}$=($2a+c$, $b$) and $\overset{ -}{n}$=($\cos B$, $\cos C$), and $\overset{ -}{m} \cdot \overset{ -}{n}$=$0$.
(1) Find the measure of angle $B$.
(2) Let $f(x) = \sin 2x \cos(A+C) - \frac{\sqrt{3}}{2} \cos 2x$, find the smallest positive period, maximum value, and the value of $x$ when $f(x)$ reaches its maximum.

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