
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
Let $y = ax^{2} + bx + 1 (a \neq 0, b$ is a real number) be a quadratic function. The values of $y$ and the corresponding values of the independent variable $x$ are shown in the table below:<br/>

| $x$ | $\ldots $ | $-1$ | $0$ | $1$ | $2$ | $3$ | $\ldots $ |
|-----|-----------|------|-----|-----|-----|-----|-----------|
| $y$ | $\ldots $ | $m$  | $1$ | $n$ | $1$ | $p$ | $\ldots $ |

$(1)$ If $m = 4$, <br/>
① Find the expression of the quadratic function; <br/>
② Write down a range of values for $x$ that satisfies the condition where $y$ decreases as $x$ increases. <br/>
$(2)$ If among the three real numbers $m$, $n$, $p$, only one is positive, find the range of values for $a$.

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