
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
When Jiaqi used the method of completing the square to derive the root formula of the quadratic equation $ax^{2}+bx+c=0\left(a\neq 0\right)$, for the case where $b^{2}-4ac \gt 0$, she did the following:<br/>Since $a\neq 0$, the equation $ax^{2}+bx+c=0$ is transformed into:<br/>$x^{2}+\frac{b}{a}x=-\frac{c}{a}$, ... Step 1<br/>$x^{2}+\frac{b}{a}x+(\frac{b}{2a})^{2}=-\frac{c}{a}+(\frac{b}{2a})^{2}$... Step 2<br/>$(x+\frac{b}{2a})^{2}=\frac{{b}^{2}-4ac}{4{a}^{2}}$... Step 3<br/>$x+\frac{b}{2a}=\frac{\sqrt{{b}^{2}-4ac}}{4a}(b^{2}-4ac \gt 0)$... Step 4<br/>$x=\frac{-b+\sqrt{{b}^{2}-4ac}}{2a}$... Step 5<br/>(1) Jiaqi's error in the solution occurs from step ______; in fact, when $b^{2}-4ac \gt 0$, the root formula for the equation $ax^{2}+bx+c=0\left(a\neq 0\right)$ is ______.<br/>(2) Solve the equation using the completing the square method: $x^{2}-2x-24=0$.

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