
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 equation of circle C is $$\begin{cases} \overset{x=5\cos\alpha }{y=-6+5\sin\alpha }\end{cases}$$ (where $\alpha$ is the parameter). A polar coordinate system is established with the origin as the pole and the positive x-axis as the polar axis.  
(1) Find the polar equation of circle C;  
(2) The polar equation of line l is $\theta=\alpha_0$, where $\alpha_0$ satisfies $\tan\alpha_0= \frac { \sqrt {5}}{2}$, l intersects C at points A and B, find the value of $|AB|$.

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