
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 sides opposite to angles $A$, $B$, $C$ are respectively $a$, $b$, $c$. If $(2a-c)\cos B=b\cos C$,  
(1) find the magnitude of angle $B$,  
(2) if $a=3$ and the area of $\triangle ABC$ is $\frac{3\sqrt{3}}{2}$, find the value of $\overrightarrow{BA}\cdot \overrightarrow{AC}$.

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