
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 that the polar coordinate equation of curve C₁ is ρ=4cosθ, establish a rectangular coordinate system xOy with the pole O as the origin and the positive semi-axis of the polar axis as the x-axis. Translate curve C₁ 2 units to the left to obtain a new curve, then halve the abscissa of each point on the new curve while keeping the ordinate unchanged to obtain curve C₂.
(I) Find the rectangular coordinate equation of curve C₂.
(II) Given that the parametric equation of line l is $$\begin{cases} x=2+2t \\ y=-1+3t \end{cases}$$ (where t is the parameter), and point Q is a moving point on curve C₂, find the maximum distance from point Q to line l.

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