
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 $Γ:\frac{{{x^2}}}{3}+\frac{{{y^2}}}{2}=1$, $B$ and $D$ are two points symmetric about the origin on the ellipse. Let $BD$ be the diagonal of a parallelogram $ABCD$ inscribed in the ellipse. If the slopes of the adjacent sides $AB$ and $BC$ are $k_{1}$ and $k_{2}$, respectively, then $k_{1}k_{2}=\_\_\_\_\_\_$.

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