
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 \( \triangle ABC \), the sides opposite to \( A, B, C \) are \( a, b, c \) respectively. Given that \( \tan C = \frac{\sin A + \sin B}{\cos A + \cos B} \) and \( \sin (B - A) = \cos C \):

1. Find \( A \) and \( C \).
2. If the area of \( \triangle ABC \) is \( S_{\triangle ABC} = 3 + \sqrt{3} \), find \( a \) and \( c \).

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