
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
One endpoint of the major axis and one of the minor axis of an ellipse is $A$ and $B$, respectively, and one of its foci closer to $A$ is $F$. At which position of the point $M$ moving along the arc $A B$ will the area of triangle $M B F$ be the largest?

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