
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

$$
\left\{\begin{array} { c } 
{ 2 t ^ { 2 } + 3 t - 9 = 0 } \\
{ \sqrt { 2 } \leq t < + \infty }
\end{array} \Leftrightarrow \left\{\begin{array}{c}
(t+3)\left(t-\frac{3}{2}\right)=0 \\
\sqrt{2} \leq t<+\infty
\end{array} \Leftrightarrow t=\frac{3}{2}\right.\right.
$$

Given (*), return to x: $x=\frac{1}{4} ; 1 ; \frac{9}{4}$.

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