
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 on a plane, the parametric equations of curve C₁ are $$\begin{cases} x=2+rcos\phi \\ y=rsin\phi \end{cases}$$ (r>0, φ is a parameter), and a polar coordinate system is established with the coordinate origin O as the pole and the positive semi-axis of the x-axis as the polar axis. The curve C₁ passes through the point $$P(2, \frac {π}{3})$$, and the polar coordinate equation of curve C₂ is ρ²(2+cos2θ)=6.
(1) Find the polar coordinate equation of curve C₁;
(2) If $$A(ρ_{1},α)，B(ρ_{2},α+ \frac {π}{2})$$ are two points on curve C₂, find the value of $$\frac {1}{|OA|^{2}}+ \frac {1}{|OB|^{2}}$$.

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