
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 acute $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively. The vectors $\overrightarrow{m}=(2a,1)$ and $\overrightarrow{n}=(\cos C,c-2b)$, and it is given that $m\perp n$.
$(1)$ Find the magnitude of angle $A$;
$(2)$ Find the range of the function $f(C)=1- \dfrac {2\cos 2C}{1+\tan C}$.

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