
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 $a$, $b$, and $c$ represent the sides opposite to angles $A$, $B$, and $C$ of $\triangle ABC$, respectively, and $\overrightarrow{m}=(a,−\sqrt {3}b)$, $\overrightarrow{n}=(\sin B,\cos A)$, if $a= \sqrt {7}$, $b=2$, and $\overrightarrow{m} \perp \overrightarrow{n}$, then the area of $\triangle ABC$ is ______.

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