
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 equation of the line is given by $\begin{cases} x=8+4t \\ y=1-t \end{cases}$ (where $t$ is the parameter). Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of the $x$-axis as the polar axis. The polar equation of the curve $C$ is $\rho^2(5-4\cos 2\theta)=9$.
(I) Find the general equation of the line $l$ and the rectangular equation of the curve $C$;
(II) Find the maximum distance from the point $M$ on the curve $C$ to the line $l$.

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