
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 the function $f(x) = 2\cos(\omega x + \phi)$ ($\omega > 0$, $0 < \phi < \frac{\pi}{2}$) has a minimum positive period of $\pi$, and the line $x = -\frac{\pi}{24}$ is a symmetry axis of its graph.  
(1) Find the values of $\omega$ and $\phi$;  
(2) In $\triangle ABC$, $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$ respectively. If $f(-\frac{A}{2}) = \sqrt{2}$, $a=3$, and $b+c=6$, find the values of $b$ and $c$.

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