
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 $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1} ($a>b>0$), M and N are the left and right vertices of the ellipse, respectively, and P is any point on the ellipse. The slopes of lines PM and PN are $k_1$ and $k_2$ ($k_1k_2 \neq 0$), respectively. If the minimum value of $|k_1|+|k_2|$ is 1, and the ellipse passes through the point ($\sqrt{3}$, $\frac{1}{2}$), find the equation of the ellipse.

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