
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 $xOy$, point $P(1,2)$ lies on line $l$ with an inclination angle of $\alpha$. Taking $O$ as the pole and the positive half-axis of $x$ as the polar axis, the equation of curve $C$ is $\rho=6\sin \theta$.
$(1)$ Write the parametric equation of line $l$ and the Cartesian equation of curve $C$;
$(2)$ Suppose line $l$ intersects curve $C$ at points $A$ and $B$, find the minimum value of $\dfrac {1}{|PA|}+ \dfrac {1}{|PB|}$.

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