
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 a parabola $y=ax^{2}+bx\left(a\neq 0\right)$ passing through point $A\left(4,4\right)$.<br/>$(1)$ When the parabola intersects the $x$-axis at point $B\left(2,0\right)$, find the expression of the parabola;<br/>$(2)$ Let the distance between the two intersection points of the parabola with the $x$-axis be $d$. When $d \gt 2$, find the range of values for $a$.

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