
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 $\begin{cases} x=3-\dfrac{\sqrt{2}}{2}t \\ y=\sqrt{5}+\dfrac{\sqrt{2}}{2}t \end{cases}$ ($t$ is the parameter). In the polar coordinate system (with the same unit length as the Cartesian coordinate system $xOy$, and the origin $O$ as the pole, and the positive $x$-axis as the polar axis), the equation of circle $C$ is $\rho =2\sqrt{5}\sin \theta$.

Find the Cartesian coordinate equations of line $l$ and circle $C$.

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