
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
(Ⅰ) If a circle $x^2+y^2=4$ is transformed under the scaling transformation $\begin{cases} x'=\lambda x \\ y'=3y \end{cases}$ ($\lambda>0$) into an ellipse with its foci on the x-axis and an eccentricity of $\frac{4}{5}$, find the value of $\lambda$;  
(Ⅱ) In the polar coordinate system, given point A(2,0), and point P moves on the curve C: $\rho= \frac{2+2\cos\theta}{\sin^{2}\theta}$, find the minimum distance between points P and A.

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