
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 an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2}=1$ ($a > b > 0$) with eccentricity $\frac{\sqrt{3}}{2}$, a line is drawn through a point $M$ on the ellipse to intersect the ellipse at points $A$ and $B$, with slopes $k_1$ and $k_2$ respectively. If points $A$ and $B$ are symmetric with respect to the origin, find the value of $k_1 \cdot k_2$.

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