
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 $ABC$, $A$, $B$, and $C$ are the three internal angles. Given that $\tan \left(\frac{A+B}{2}\right) + \tan \left(\frac{C}{2}\right) = \frac{4\sqrt{3}}{3}$:
1. If $\sin B \cdot \sin C = \cos^2 \left(\frac{A}{2}\right)$, find the values of $A$, $B$, and $C$.
2. If $C$ is an acute angle, find the range of values for $\sin A + \sin B$.

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