
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 plane rectangular coordinate system $xOy$, the parametric equations of curve $C$ are $\left\{\begin{array}{l}{x=\frac{4}{1+{t}^{2}}},\\{y=\frac{4t}{1+{t}^{2}}}\end{array}\right.$ $(t\in R)$.<br/>$(Ⅰ)$ Find the rectangular coordinate equation of curve $C$;<br/>$(Ⅱ)$ Given that the parametric equations of line $l$ are $\left\{\begin{array}{l}{x=1+\sqrt{3}t,}\\{y=t}\end{array}\right.$ $(t\in R)$, point $M(1,0)$, and line $l$ intersects curve $C$ at points $A$ and $B$, find $\frac{1}{|MA|}+\frac{1}{|MB|}$.

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