
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 that \( M \) is an arbitrary point on the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 (a>b>0)\), \( F_{1} \) and \( F_{2} \) are the left and right foci of the ellipse, respectively. The lines \( M F_{1} \) and \( M F_{2} \) intersect the ellipse at points \( A \) and \( B \), respectively. Then \(\frac{b^{2}}{a^{2}}\left(\frac{\left|MF_{1}\right|}{\left|F_{1}A\right|}+\frac{\left|MF_{2}\right|}{\left|F_{2}B\right|}+2\right)=\) ______.

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