
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 the ellipse $\frac {x^{2}}{9} + \frac {y^{2}}{4} = 1$, and the line $L: x + 2y - 10 = 0$.

(1) Does there exist a point $M$ on the ellipse for which the distance to line $L$ is minimal? If so, find the coordinates of point $M$ and the minimum distance.

(2) Does there exist a point $P$ on the ellipse for which the distance to line $L$ is maximal? If so, find the coordinates of point $P$ and the maximum distance.

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