
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 ellipse $C: 9x^2 + y^2 = 1$, a line $l$ does not pass through the origin $O$ and is not parallel to the coordinate axes. Line $l$ intersects $C$ at two points $A$ and $B$, and the midpoint of segment $AB$ is $M$. Then the product of the slope of line $OM$ and the slope of line $l$ is \_\_\_\_\_\_.

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