
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 $ABC$, with angles $A$, $B$, and $C$ opposite to sides $a$, $b$, and $c$ respectively, it is known that $\dfrac {a}{c}\cos B + \dfrac {b}{c}\cos A = \dfrac {\sqrt{3}}{2\cos C}$  
(I) Find the magnitude of $\angle C$;  
(II) Find the minimum value of $\sin B - \sqrt{3}\sin A$.

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