
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 Cartesian coordinate system, define d(A, B) = |x₁ - x₂| + |y₁ - y₂| as the "rectangular distance" between two points A(x₁, x₂) and B(y₁, y₂). Given a line l that passes through point P($\sqrt{5}$, 0) with an inclination angle α, where cosα = -$\frac{\sqrt{5}}{5}$, and a line segment EF is intercepted on line l with x-coordinates ranging from -$\sqrt{5}$ to $2\sqrt{5}$. Find the sum of the minimum and maximum "rectangular distance" from the origin O to any point on the line segment EF.

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