
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 points A(-3, 0) and B(3, 0), lines AM and BM intersect at point M, and the product of their slopes is $\frac{16}{9}$.
(I) Find the trajectory equation of point M;
(II) If point P(4, 2) and F(5, 0), find the minimum value of |MP| + |MF|.

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