
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 quadratic function $y=ax^{2}+bx+c$, the values of the independent variable $x$ and the corresponding function values $y$ are as shown in the table: 

| $x$ |  | $-2$ | $-1$ | $0$ | $1$ | $2$ | $3$ |  |
|-----|-----------|------|------|----|-----|-----|-----|----------|
| $y$ |  | $8$  | $3$  | $0$ | $-1$| $0$ | $3$ |  |

Determine the range of values of $x$ in the real number system for which $y-3 > 0$ holds.

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