
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
(Optional Course 4-4: Coordinate Systems and Parametric Equations) Given that the parametric equation of the curve $C$ is $ \begin{cases} x=a\cos \phi \\ y= \sqrt {3}\sin \phi \end{cases} (\phi \text{ is the parameter}, a > 0)$, and the parametric equation of the line $l$ is $ \begin{cases} x=3+t \\ y=-1-t \end{cases} (t \text{ is the parameter})$, the curve $C$ and the line $l$ have a common point on the $x$-axis. Establish a coordinate system with the coordinate origin as the pole and the positive half of the $x$-axis as the polar axis.
(I) Find the general equation of the curve $C$;
(II) If points $A(ρ_{1},θ),B(ρ_{2},θ+ \dfrac {2π}{3}),C(ρ_{3},θ+ \dfrac {4π}{3})$ are on the curve $C$, find the value of $\dfrac {1}{|OA|^{2}}+ \dfrac {1}{|OB|^{2}}+ \dfrac {1}{|OC|^{2}}$.

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