
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 $$\begin{cases} x= \sqrt {3}\cos a \\ y=\sin a\end{cases}$$ (where a 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. The polar equation of the curve C₂ is θ=a (ρ∈R). After rotating C₂ counterclockwise by $$\frac {π}{2}$$, we obtain the curve C₃.

1. Write the polar equations of C₁ and C₃.
2. Suppose C₂ and C₃ intersect the curve C₁ at points A, B and C, D, respectively. Find the range of values for the area of the quadrilateral ACBD.

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