
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, with the origin O as the pole and the positive half-axis of the x-axis as the polar axis, a polar coordinate system is established. The polar coordinates of point A are $(3, \frac{\pi}{2})$, and the polar coordinates of point B are $(6, \frac{\pi}{6})$. The curve C is defined by $(x-1)^2+y^2=1$.

(1) Find the polar equations of curve C and line AB;  
(2) A ray l passing through point O intersects curve C at point M and line AB at point N. If $|OM|\cdot|ON|=2$, find the equation of the line containing ray l in Cartesian coordinates.

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