
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 Cartesian coordinate system \(xOy\), the equation of the ellipse \(C\) is given by the parametric form:
\[
\begin{cases}
x=5\cos\varphi \\
y=3\sin\varphi
\end{cases}
\]
where \(\varphi\) is the parameter.
(I) Find the general equation of the straight line \(l\) that passes through the right focus of the ellipse and is parallel to the line represented by the parametric equations 
\[
\begin{cases}
x=4-2t \\
y=3-t
\end{cases}
\]
where \(t\) is the parameter.
(II) Find the maximum area of the inscribed rectangle \(ABCD\) in ellipse \(C\).

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