
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 line $l$: $x-2y-2\sqrt{5}=0$ intersects the $x$ and $y$ axes at points $M$ and $N$, respectively. $P$ is any point on circle $C$: $x^{2}+y^{2}=2$.

(I) Find the minimum area of $\triangle PMN$.
(II) Find the probability that the distance from point $P$ to line $l$ is less than $1$.

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