
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 the line l: $$\left\{\begin{array}{l}x=1+ \frac{1}{2}t \\ y= \frac{ \sqrt{3}}{2}t\end{array}\right.$$ (t is a parameter), and the curve C₁: $$\left\{\begin{array}{l}x=cosθ \\ y=sinθ\end{array}\right.$$ (θ is a parameter).

1. The line l intersects the curve C₁ at points A and B. Find the length |AB|.
2. The curve C₂ is defined as: $$\left\{\begin{array}{l}x= \frac{1}{2}cosθ \\ y= \frac{ \sqrt{3}}{2}sinθ\end{array}\right.$$ (θ is a parameter). Point P is a moving point on curve C₂. Find the minimum distance from point P to line l.

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