
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 vectors $\overset{\to }{m}\,=(\sin A,\cos A)$, $\overset{\to }{n}\,=(\sqrt{3},-1)$, and $\overset{\to }{m}\,\bullet \overset{\to }{n}\,=1$, where $A$ is an acute angle.

(1) Find the value of angle $A$;

(2) Find the range of the function $f(x)=\cos 2x+4\cos A\sin x(x\in \mathbb{R})$.

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