
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 $l$ passes through the point $M(-1,0)$ and intersects the ellipse ${{x}^{2}}+2{{y}^{2}}=4$ at two points, ${{P}_{1}}$ and ${{P}_{2}}$. Let $P$ be the midpoint of the line segment ${{P}_{1}}{{P}_{2}}$. If the slope of the line $l$ is ${{k}_{1}}\,(\ne 0)$ and the slope of the line $OP$ is ${{k}_{2}}$, then find the product ${{k}_{1}}{{k}_{2}}$.

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