
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 $((x+6)^{2}+y^{2}=25)$.

(1) Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of the $x$-axis as the polar axis. Derive the polar coordinate equation of $C$;

(2) The parametric equations of line $l$ are $\begin{cases} x=t\cos \alpha, \\ y=t\sin \alpha \end{cases}$ ($t$ is the parameter). $l$ intersects $C$ at points $A$ and $B$ with $|AB| = \sqrt{10}$. Determine the slope of $l$.

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