
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 $\dfrac {\sin ( \dfrac {\pi}{2}-\alpha)+\sin (-\pi-\alpha)}{3\cos (2\pi+\alpha)+\cos ( \dfrac {3\pi}{2}-\alpha)}=3$.  
(I) Find the value of $\dfrac {\sin \alpha-3\cos \alpha}{\sin \alpha+\cos \alpha}$;  
(II) If the center of circle $C$ is on the $x$-axis, and the distance from the center to the line $y=\tan \alpha \cdot x$ is $2 \sqrt {5}$, and the chord intercepted by the line $y=\tan \alpha \cdot x$ on circle $C$ is $8$, find the standard equation of circle $C$.

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