
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 equations of the curve C₁ are $$\begin{cases} x=\cos t, \\ y=2\sin t, \end{cases}$$ (where t is the parameter). Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of the x-axis as the polar axis, ensuring it has the same unit length as the rectangular coordinate system xOy. The equation of the straight line l in rectangular coordinates is $$y=\sqrt{3}x$$.

1. Find the polar equation of the curve C₁.
2. If the polar equation of the curve C₂ is ρ + 8cosθ = 0, and it intersects with the straight line l at point A in the third quadrant, while the straight line l intersects with C₁ at point B in the first quadrant, find the length |AB|.

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