
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 $x$ as the polar axis. Find the polar equation of $C$.
2. The polar equation of line $l$ is $\theta = \alpha$ ($\rho \in \mathbb{R}$). $l$ intersects $C$ at points $A$ and $B$, and $|AB| = \sqrt{10}$. Find the slope of $l$.

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