
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
A line passing through point $M(-2,0)$ intersects with the ellipse $\frac{x^2}{2} + y^2 = 1$ at points $P_1$ and $P_2$, and the midpoint of the line segment $P_1P_2$ is $P$. Let the slope of line $l$ be $k_1$ ($k_1 \neq 0$), and the slope of line $OP$ ($O$ is the origin) 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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