
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 xOy, the parametric equations of the line l are $\left\{\begin{array}{l}x=\sqrt{3}+t\\ y=6-\sqrt{3}t\end{array}\right.$ (where t is a parameter). A circle C passes through the pole and its polar coordinates of the center are $（2,\frac{π}{2}）$. <br /> (1) Find the polar coordinate equation of circle C; <br /> (2) If the ray $θ=\frac{π}{3}（ρ≥0）$ intersects circle C and line l at points A and B (point A is different from the origin O), find the length of segment AB.

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