
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 a point $M$ moving on the circle $x^{2}+y^{2}=4$, and point $N(4,0)$, let point $P$ be the midpoint of segment $MN$  
$(1)$ Find the equation of the trajectory of point $P$;  
$(2)$ Find the maximum and minimum values of the distance from point $P$ to the line $3x+4y-26=0$.

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