
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 equation of circle $C$ is $(x-2)^2 + y^2 = 9$.
(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 parametric equations of line $L$ are given by $x = t\cos{\alpha}, y = t\sin{\alpha}$, where $t$ is a parameter. $L$ intersects $C$ at points $A$ and $B$, and $|AB| = 2\sqrt{7}$. Find the slope of $L$.

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