
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 that the line $y=m (m>0)$ is a tangent line to the graph of the function $f(x)=\sqrt{3}\cos^2{\omega x} - \sin{\omega x}\cos{\omega x} - \frac{\sqrt{3}}{2} (\omega > 0)$, and the x-coordinates of the tangent points form an arithmetic sequence with a common difference of $\pi$.
(I) Find the values of $\omega$ and $m$;
(II) In $\triangle ABC$, $a$, $b$, and $c$ are the lengths of the sides opposite to angles $A$, $B$, and $C$, respectively. If $(\frac{A}{2}, 0)$ is a center of symmetry of the graph of $f(x)$, and $a=4$, find the maximum value of $b+c$.

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