
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) A circle $x^{2}+y^{2}=4$ undergoes a stretch transformation $\begin{cases} x'=\lambda x \ y'=3y \end{cases}(\lambda > 0)$ and becomes an ellipse with a focus on the $x$-axis and an eccentricity of $\frac{4}{5}$. Find the value of $\lambda$.
(II) In a polar coordinate system, given point $A(2,0)$, 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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