
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 $ \triangle ABC $, let $a$, $b$, and $c$ represent the lengths of the sides opposite angles $A$, $B$, and $C$ respectively, and let vectors $\overrightarrow {m}=(\cos A, \sin A)$ and $\overrightarrow {n}=(\cos B, \sin B)$. It is known that $\overrightarrow {m} \cdot \overrightarrow {n} = \sqrt {3}\sin B - \cos C$.  
(1) Find the magnitude of angle $A$.  
(2) If $a=3$, find the maximum area of triangle $ABC$.

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