
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 origin O as the pole and the positive semi-axis of the x-axis as the polar axis, establish a polar coordinate system. The polar coordinates of point M are (2, β), and the polar equation of curve C is ρ=2sinθ, θ∈[0,2π).
(1) Find the rectangular coordinate equation of curve C;
(2) The chord length obtained by the intersection of the line passing through the pole O and point M with curve C is $\sqrt {3}$, find the value of β and the ratio of the two arc lengths into which the line OM divides curve C.

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