
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 $x\in C(\text{set of all complex numbers})$, the equation about $x$ is $x^{2}+tx+2=0\left(t\in R\right)$, and the two roots are $x_{1}$ and $x_{2}$. If $|x_{1}-x_{2}|=2\sqrt{2}$, find the possible values of $t$.

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