
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 a non-isosceles triangle \( \triangle ABC \), the sides opposite to \(\angle A\), \(\angle B\), and \(\angle C\) are \(a\), \(b\), and \(c\) respectively, and they satisfy the equation:
\[
(2c - b) \cos C = (2b - c) \cos B.
\]
(1) Find the measure of \(\angle A\).  
(2) If \(a = 4\), determine the range of the area of \(\triangle ABC\).

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