
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, there is a ray l: $$y= \sqrt {3}x$$ (x≥0), curve C₁ with parametric equations $$\begin{cases} \overset{x=3cos\alpha }{y=2sin\alpha }\end{cases}$$ (α is the parameter), and curve C₂ with the equation x²+(y-2)²=4. In the polar coordinate system with the origin as the pole and the non-negative half of the x-axis as the polar axis, curve C₃ has the polar equation ρ=8sinθ.

1. Write the polar equation of ray l and the Cartesian equation of curve C₁.
2. Given that ray l intersects with C₂ at points O and M, and with C₃ at points O and N, find the value of |MN|.

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