
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 the rectangular coordinate system $(xOy)$, the parametric equations of line $l$ are $\begin{cases} x=2+\frac{1}{2}t \\ y=\frac{\sqrt{3}}{2}t \end{cases}$ ($t$ is the parameter). If the origin $O$ is taken as the pole and the positive semi-axis of $x$ as the polar axis to establish a polar coordinate system, the polar equation of the curve $C$ is $\rho\sin^2\theta-4\cos\theta=0$.

(1) Find the ordinary equations of line $l$ and curve $C$.

(2) Given that line $l$ intersects curve $C$ at points $A$ and $B$, and $M(2,0)$, find the value of $|\frac{1}{|MA|}-\frac{1}{|MB|}|$.

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