
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]


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Selected Exercise $(4-4)$: Coordinate Systems and Parametric Equations

In the rectangular coordinate system $(xOy)$, the parametric equations of curve $C$ are given by $\begin{cases} & x=4t^2 \\ & y=4t \\ \end{cases} (t\text{ is the parameter})$, and the polar coordinate equation of line $l$ is $\rho(\cos \theta-\sin \theta)=4$. The curve $C$ intersects with line $l$ at points $A$ and $B$.

(I) Find the Cartesian equation of curve $C$ and line $l$ in the rectangular coordinate system.

(II) Find the area of triangle $AOB$.

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