
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
Let $\triangle ABC$ have sides $a$, $b$, and $c$ opposite to angles $A$, $B$, and $C$, respectively. Given that $\frac{\sin C}{\sin A + \sin B} + \frac{b}{a+c} = 1$. Find:<br/>
$(1)$ The measure of angle $\angle A$;<br/>
$(2)$ If $|\overrightarrow{CB}-\overrightarrow{CA}|=4$ and $\cos B + \cos C = 1$, find the area of $\triangle ABC$.

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