
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 point \( A(-2,2) \), point \( B \) is a moving point on the ellipse \( \frac{x^{2}}{25}+\frac{y^{2}}{16}=1 \), and \( F \) is the left focus. Find the coordinates of \( B \) when \( |AB| + \frac{5}{3}|BF| \) is minimized.

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