
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
Read the following material:<br/>Example: Solve the equation $x^{2}-|x|-2=0$.<br/>Solution: Discuss in two cases:<br/>① When $x\geqslant 0$, the original equation is $x^{2}-x-2=0$.<br/>Solving gives $x_{1}=2$, $x_{2}=-1$ (not satisfying the condition, discard);<br/>② When $x \lt 0$, the original equation is $x^{2}+x-2=0$.<br/>Solving gives $x_{3}=-2$, $x_{4}=1$ (not satisfying the condition, discard).<br/>Therefore, the roots of the original equation are $x=\pm 2$.<br/>Please refer to the example and solve the equation: $x^{2}-|x-1|-3=0$.

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