
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
Given that the sides \(a\), \(b\), and \(c\) of a triangle \(\triangle ABC\) opposite to the interior angles \(\angle A\), \(\angle B\), and \(\angle C\) respectively, form a geometric progression, determine the range of values of \(\frac{\sin A \cdot \cot C + \cos A}{\sin B \cdot \cot C + \cos B}\).

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