
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 P on the ellipse $\frac{x^{2}}{9}+\frac{y^{2}}{5}=1$, and points M and N on the circles $(x+2)^{2}+y^{2}=1$ and $(x-2)^{2}+y^{2}=1$ respectively, find the minimum and maximum values of $|PM|+|PN|$.

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