
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 that the graph of the quadratic function $y_1=x^2+bx-3$ intersects the line $y_{2}=x+1$ at points $A(-1,0)$ and $C(4,m)$.<br/>$(1)$ Find the expression of $y_{1}$ and the value of $m$;<br/>$(2)$ When $y_{1} \gt y_{2}$, directly write down the range of the independent variable $x$.

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