
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 $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. It is known that $a( \sqrt {3}\tan B-1)= \dfrac {b\cos A}{\cos B}+ \dfrac {c\cos A}{\cos C}$.  
$(1)$ Find the size of angle $C$;  
$(2)$ If the perimeter of the triangle is $20$ and the area is $10 \sqrt {3}$, and $a > b$, find the lengths of the sides of the triangle.

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