
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 parametric equations of curve C₁ as $$\left\{\begin{array}{l}x= \sqrt{2}\cosθ \\ y=\sinθ\end{array}\right.$$ (where θ is the parameter), and the polar coordinate equation of curve C₂ as ρsin²θ=4cosθ, established with the origin O of the rectangular coordinate system as the pole and the positive semi-axis of x as the polar axis.

1. Find the ordinary equation of C₁ and the rectangular coordinate equation of C₂.
2. If the line l passing through point F(1,0) intersects with C₁ at points A and B, and with C₂ at points M and N, find the range of values for $$\frac{|FA||FB|}{|FM||FN|}$$.

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