
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 $\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1$, and points $M$, $N$ on the circles $(x+3)^{2} + y^{2} = 4$ and $(x-3)^{2} + y^{2} = 1$, respectively. Find the minimum and maximum values of $|PM| + |PN|$.

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