
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 the ellipse $\frac{x^{2}}{4}+\frac{y^{2}}{3}=1$ with a point $P(1,-1)$ inside it and $F$ being the right focus of the ellipse, find the point $M$ on the ellipse such that the value of $|M P| + 2|M F|$ is minimized.

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