
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 $\Delta ABC$, the sides opposite to angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$, respectively. If $a\sin B=b\cos A$,

(Ⅰ) Find $A$;

(Ⅱ) Let the function $f(x)=\sqrt{3}\sin x\cos x-{\cos }^{2}x$ $(x\in \mathbb{R})$, find the range of $f(B)$.

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