
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 line $l$ is
$$
\begin{cases}
x=2+t\cos \alpha \\
y=1+t\sin \alpha
\end{cases}
(t \text{ is the parameter}),
$$
In the polar coordinate system (which uses the same unit length as the Cartesian coordinate system $xOy$, with the origin as the pole and the positive $x$-axis as the polar axis), the equation of circle $C$ is $\rho = 6\cos \theta$.

(1) Find the Cartesian coordinate equation of circle $C$.

(2) Suppose circle $C$ intersects line $l$ at points $A$ and $B$. If point $P$ has coordinates $(2,1)$, find the minimum value of $|PA|+|PB|$.

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