
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 that the perimeter of $\triangle ABC$ is $\sqrt{3} + 1$, and $\sin B + \sin C = \sqrt{3}\sin A$.

$(1)$ Find the length of side $BC$;

$(2)$ If the area of $\triangle ABC$ is $\frac{1}{3}\sin A$, find the degree measure of angle $A$.

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