
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
In the Cartesian coordinate system $xOy$, it is known that the parabola $y=ax^{2}+bx-4$ passes through the point $A(-4,0)$ and has the axis of symmetry $x=-1$.  
$(1)$ Find $a$ and $b$;  
$(2)$ The parabola intersects the $y$-axis at point $B$. If the line $AB$ is moved down by $m$ units $(m > 0)$ and exactly intersects the parabola at one point, find the value of $m$.

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