
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 the triangle \( \triangle ABC \), the side lengths \( a, b, c \) opposite to angles \( \angle A, \angle B, \angle C \) respectively form a geometric sequence,

\[ 2 \cos (A - C) - 2 \cos B = 1 \]

Extend \( BC \) to point \( D \) such that \( BD = 5 \). Find:
(1) The measure of \( \angle B \);
(2) The range of values for \( \overrightarrow{AC} \cdot \overrightarrow{CD} \).

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