
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 $ABC$, the internal angles $A$, $B$, $C$ are opposite to the sides $a$, $b$, $c$ respectively. The vectors $\overrightarrow{m}=(a, \sqrt {3}b)$ and $\overrightarrow{n}=(\sin B,-\cos A)$, and $\overrightarrow{m}\cdot \overrightarrow{n}=0$.
$(1)$ Find $A$;
$(2)$ If $a= \frac {7}{2}$ and the area of $\triangle ABC$ is $\frac {3}{2} \sqrt {3}$, find the value of $b+c$.

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