
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
Given the parametric equation of the parabola $M$ as $$\begin{cases} x=t \\ y=t^{2}\end{cases}$$ (where $t$ is the parameter), in the Cartesian coordinate system $xOy$, with $O$ as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. The equation of circle $N$ is $\rho^{2}-6\rho\sin\theta=-8$. Find the equation of the line in Cartesian coordinates that passes through the focus of the parabola $M$ and the center of circle $N$.

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