
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 given by $$\begin{cases} x=t\cos\alpha \\ y=1+t\sin\alpha \end{cases}$$, and the polar coordinate equation of the curve C2 with the origin O as the pole and the positive semi-axis of the x-axis as the polar axis is ρ=2cosθ.

1. If the parameter of curve C1 is α, and C1 intersects C2 at exactly one point, find the Cartesian equation of C1.
2. Given point A(0, 1), if the parameter of curve C1 is t, 0<α<π, and C1 intersects C2 at two distinct points P and Q, find the maximum value of $$\frac {1}{|AP|}+\frac {1}{|AQ|}$$.

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