
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 hyperbola $y^2 - \frac{x^2}{2} = 1$ and a line $l$ that does not pass through the origin $O$ and is not parallel to the coordinate axes, intersecting at points $M$ and $N$, with the midpoint of segment $MN$ being $P$. Let the slope of line $l$ be $k_1$ and the slope of line $OP$ be $k_2$, calculate the product of $k_1$ and $k_2$.

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