
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 $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ in $\triangle ABC$, respectively, and vectors $\overrightarrow{m}=(a, \frac{\sqrt{3}}{3}b)$, $\overrightarrow{n}=(\cos A,\sin B)$, it is known that $\overrightarrow{m}$ and $\overrightarrow{n}$ are collinear.

$(1)$ Find the magnitude of angle $A$;

$(2)$ If $a= \sqrt{7},b= \sqrt{3}$, find the area of $\triangle ABC$.

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