
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 $$\begin{cases} x=2-3t \\ y= \sqrt {3}t\end{cases}$$ (t is the parameter). Establish a polar coordinate system with the coordinate origin O as the pole and the positive semi-axis of the x-axis as the polar axis. The polar coordinate equation of the curve C₁ is ρ=4cosθ.

1. Find the polar coordinate equation of l and the rectangular coordinate equation of C₁.
2. If the polar coordinate equation of the curve C₂ is θ= $$\frac {π}{6}$$, the intersection point of C₂ and l is A, and the intersection point of C₁ and C₂ that is different from the pole is B, find |AB|.

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