
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 the curve $C$ defined by
$$
\begin{cases}
x = 3\cos\theta, \\
y = 2\sin\theta,
\end{cases}
$$
and the line $l$ with the polar equation $\rho(\cos\theta - 2\sin\theta) = 12$:
1. Convert the polar equation of line $l$ into a Cartesian coordinate equation;
2. Let point $P$ lie on curve $C$. Find the minimum distance from point $P$ to line $l$.

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