
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 a triangle \( \triangle ABC \) with interior angles \( A, B, \) and \( C \) opposite sides \( a, b, \) and \( c \) respectively, and the equation \( \sqrt{3} b \cos \frac{A+B}{2} = c \sin B \):

1. Find the measure of \( \angle C \).
2. If \( a + b = \sqrt{3} c \), find \( \sin A \).

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