
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
Given that the pole of the polar coordinate system coincides with the origin of the Cartesian coordinate system, and the polar axis coincides with the positive half-axis of the x-axis. If the polar equation of line $l$ is $\rho\cos(\theta- \frac{\pi}{4})=3\sqrt{2}$,  
(1) Convert the polar equation of line $l$ into a Cartesian coordinate equation;  
(2) Given that $P$ is a point on the curve $C: \frac{x^{2}}{16}+ \frac{y^{2}}{9}=1$, find the minimum distance from point $P$ to line $l$.

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