
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 $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1$ with an eccentricity of $\frac{\sqrt{2}}{2}$, a line $MA$ is drawn through a point $M$ on the ellipse, intersecting the ellipse at points $A$ and $B$ with slopes $k_{1}$ and $k_{2}$, respectively. If points $A$ and $B$ are symmetric about the origin, find the value of $k_{1} \cdot k_{2}$.

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