
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 \( \triangle ABC \), let the sides opposite to angles \( \angle A \), \( \angle B \), and \( \angle C \) be \( a \), \( b \), and \( c \) respectively, satisfying \( a \cos C = (2b - c) \cos A \).
1. Find the measure of \( \angle A \).
2. If \( a = \sqrt{3} \), and \( D \) is the midpoint of side \( BC \), determine the range of values for \( AD \).

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