
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 that the corresponding values of the abscissa $x$ and ordinate $y$ of some points on the graph of the parabola $y=x^{2}+mx+n$ are shown in the table below:<br/>

| $x$ | $\ldots $ | $-5$ | $-3$ | $-1$ | $1$ | $3$ | $\ldots $ |
|-----|-----------|------|------|------|-----|-----|-----------|
| $y$ | $\ldots $ | $6$  | $-4$ | $-6$ | $0$ | $14$| $\ldots $ |

Find the coordinates of the intersection points of the graph of the parabola with the $y$-axis.

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