
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
In the Cartesian coordinate system, two circles $O_1$ and $O_2$ are tangent to the x-axis, and their centers $O_1$ and $O_2$ are collinear with the origin $O$. The product of the x-coordinates of points $O_1$ and $O_2$ is 6. Let circles $O_1$ and $O_2$ intersect at points $P$ and $Q$. Given the line $l: 2x - y - 8 = 0$, find the minimum distance between point $P$ and any point $M$ on line $l$.

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