
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 rectangular coordinate system xOy, the parametric equation of line l is $$\begin{cases} x=1+t \\ y=-3+t \end{cases}$$ (where t is the parameter), and the polar coordinate system is established with the origin O as the pole and the positive semi-axis of the x-axis as the polar axis. The polar equation of curve C is ρ=6cosθ.
(I) Find the general equation of line l and the rectangular coordinate equation of curve C.
(II) If line l intersects curve C at points A and B, find the area of triangle ABC.

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