
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 $A$, $B$, $C$ are $a$, $b$, $c$ respectively. The point $(a, b)$ lies on the line $x(\sin A - \sin B) + y \sin B = c \sin C$.

(I) Find the value of angle $C$;

(II) If $2\cos ^{2} \frac {A}{2}-2\sin ^{2} \frac {B}{2}= \frac { \sqrt {3}}{2}$, and $A < B$, find $\frac {c}{a}$.

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