
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 $\triangle ABC$, the sides opposite angles $A$, $B$, $C$ are respectively $a$, $b$, $c$, and vectors $\overrightarrow{m}=(a,-2b-c)$, $\overrightarrow{n}=(\cos A,\cos C)$, and $\overrightarrow{m} \parallel \overrightarrow{n}$.  
$(I)$ Find the magnitude of angle $A$;  
$(II)$ Find the maximum value of $2 \sqrt {3}\cos ^{2} \frac {C}{2}-\sin (B- \frac {\pi}{3})$ and the magnitudes of angles $B$, $C$ when the maximum value is attained.

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