
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, a polar coordinate system is established with the origin as the pole and the non-negative half-axis of the x-axis as the polar axis. The parametric equations of curve C are
$$
\begin{cases}
x = 2\cos\theta \\
y = \sin\theta
\end{cases}
$$
(θ parameter), and the polar equation of line L is $\rho = \frac{3\sqrt{2}}{\cos\theta + 2\sin\theta}$.

(Ⅰ) Write the standard equation of curve C and the Cartesian equation of line L.

(Ⅱ) Let P be a point on curve C, find the minimum distance from P to line L.

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