
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 \( \triangle ABC \), \( BC = a \), \( CA = b \), and \( AB = c \). If \( b \) is the geometric mean of \( a \) and \( c \), and \( \sin A \) is the arithmetic mean of \( \sin (B - A) \) and \( \sin C \), find the value of \( \cos B \).

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