
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 that the parametric equation of curve $C_1$ is $ \begin{cases} x=1+\frac{1}{2}t \\ y=\frac{\sqrt{3}}{2}t \\ \end{cases} (t $ is the parameter$)$. In the polar coordinate system with the origin as the pole and the positive half of the x-axis as the polar axis, the curve $C_2$ is defined as $ρ^2=\frac{12}{3+\sin^2θ}$.

(I) Find the ordinary equation of curve $C_1$ and the rectangular coordinate equation of $C_2$;

(II) If $C_1$ and $C_2$ intersect at points $A$ and $B$, and point $F(1,0)$, find the value of $\frac{1}{|FA|}+\frac{1}{|FB|}$.

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