
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 \( A(-2,2) \), let \( P \) be a moving point on the ellipse \( \frac{x^{2}}{25}+\frac{y^{2}}{16}=1 \). Define \( F \) as the left focus of the ellipse. Find the minimum value of \( |P A|+\frac{5}{3}|P F| \) and the coordinates of point \( P \).

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