
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 $\triangle ABC$, the sides opposite angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. The vectors $\overrightarrow{m} = (2b - c, a)$ and $\overrightarrow{n} = (\cos C, \cos A)$, and $\overrightarrow{m} \parallel \overrightarrow{n}$.
(1) Find the measure of angle $A$.
(2) If $\overrightarrow{AB} \cdot \overrightarrow{AC} = 4$, find the minimum value of side $a$.

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