
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 $a, b, c$ of the triangle $\triangle ABC$ are in geometric progression, and the angles opposite these sides are $\angle A, \angle B, \angle C$ respectively. Determine the range of values for $\sin B + \cos B$.

(A) $\left[\frac{1}{2}, 1+\frac{\sqrt{3}}{2}\right]$

(B) $(1, \sqrt{2}]$

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