
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 equation of circle $C$ is $(x+6)^{2}+y^{2}=25$.
(I) Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis, and derive the polar equation of $C$;
(II) The parametric equations of line $l$ are given by $ \begin{cases} x=t\cos \alpha \\ y=t\sin \alpha \end{cases} (t\text{ is the parameter})$, where $\alpha$ is the inclination angle of line $l$. Line $l$ intersects with $C$ at points $A$ and $B$, and $|AB|= \sqrt {10}$, find the slope of $l$.

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