
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 $\triangle ABC$, the three internal angles $A$, $B$, and $C$ form an arithmetic sequence.
1. If $\sin^2 B = \sin A \sin C$, determine the shape of $\triangle ABC$.
2. If $\triangle ABC$ is an obtuse triangle and $a > c$, find the range of values for $\sin^2 \frac{C}{2} + \sqrt{3}\sin \frac{A}{2} \cos \frac{A}{2} - \frac{1}{2}$.

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