
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 sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and $\frac{\sin C}{\cos C} = \frac{\sin A + \sin B}{\cos A + \cos B}$, $\sin(B - A) + \cos(A + B) = 0$.

1. Find the value of $\sin B$.
2. If the area of $\triangle ABC$ is $3 + \sqrt{3}$, find the values of $a$ and $c$.

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