
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 $l$ passing through point $M(-2,0)$ intersects the ellipse $x^2 + 2y^2 = 4$ at two points $P_1$ and $P_2$. Let the midpoint of segment $P_1P_2$ be $P$. Suppose the slope of line $l$ is $k_1$ (with $k_1 \neq 0$) and the slope of line $OP$ is $k_2$, calculate the product $k_1k_2$.

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