
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
A quadratic function $y=ax^{2}+bx+c$ has some corresponding values of the independent variable $x$ and the function value $y$ as shown in the table below:

| $x$ | $\ldots $ | $-1$ | $0$ | $1$ | $2$ | $3$ | $\ldots $ |
|-----|-----------|------|-----|-----|-----|-----|-----------|
| $y$ | $\ldots $ | $-1$ | $-\dfrac{7}{4}$ | $-2$ | $-\dfrac{7}{4}$ |       | $\ldots $ |

Based on the information in the table, complete the following questions:

1. When $x=3$, $y=$______;
2. When $x=$______ , $y$ has a minimum value of ________ at $y=$______;
3. If points $A(x_{1}, y_{1})$ and $B(x_{2}, y_{2})$ are two points on the graph of the quadratic function, and $-1 < x_{1} < 0$, $1 < x_{2} < 2$, compare the values of the two functions: $y_{1}$______$y_{2}$;
4. If the independent variable $x$ ranges from $0\leq x\leq 5$, then the range of function values $y$ is ________.

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