
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 that point $M(x_{0},y_{_{0}})$ moves on the circle $C$: $x^{2}+y^{^{2}}=4$, point $N(4,0)$, and point $P(x,y)$ is the midpoint of segment $MN$,
(I) Find the trajectory equation of point $P(x,y)$;
(II) Find the maximum and minimum values of the distance from point $P(x,y)$ to the line $3x+4y-26=0$.

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