
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 $$\begin{cases} x=t\cos\alpha \\ y=t\sin\alpha \end{cases}$$ (t is a parameter and t>0, α∈(0, $$\frac {π}{2}$$)), and the parametric equations of the curve C₂ are $$\begin{cases} x=\cos\beta \\ y=1+\sin\beta \end{cases}$$ (β is a parameter and β∈(- $$\frac {π}{2}$$, $$\frac {π}{2}$$)). Establish a polar coordinate system with O as the pole and the positive semi-axis of the x-axis as the polar axis. The polar coordinate equation of the curve C₃ is ρ=1+cosθ (θ∈(0, $$\frac {π}{2}$$)), and the polar coordinate equation of the curve C₄ is ρcosθ=1.
(I) Find the distance from the intersection point of C₃ and C₄ to the pole.
(II) Suppose C₁ and C₂ intersect at point P, and C₁ and C₃ intersect at point Q. Find the maximum value of |OP|+|OQ| when α varies on (0, $$\frac {π}{2}$$).

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