
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, 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 parametric equations of the curve C₁ are given by $$\begin{cases} x= \sqrt {3}cosα \\ y=sinα\end{cases}$$ (where α is the parameter), and the polar coordinate equation of the curve C₂ is ρ(cosθ + sinθ) = 15.
(1) Write the ordinary equation of C₁ and the rectangular coordinate equation of C₂;
(2) If points P and Q are any points on curves C₁ and C₂ respectively, find the minimum value of |PQ| and the coordinates of P at this time.

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