
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
"Through equivalent transformation, unfamiliar becomes familiar, and unknown becomes known" is the basic way of thinking in solving problems in mathematics. For example, to solve the equation $x-\sqrt{x}=0$, one can use this way of thinking by letting $\sqrt{x}=y$, transforming the original equation into $y^{2}-y=0$, a familiar one-variable quadratic equation in terms of $y. Solve for $y$, then find $x$. This method is also known as "substitution method". Xiao Ming used this way of thinking and the substitution method to solve the equation $2\sqrt{x}-3=0$ and found the solution. Please follow his method to find the solutions for the other two equations below and fill in your solution process in the table provided below.

| Equation | New Equation by Substitution | Solve New Equation | Check | Find Solution for Original Equation |
|----------|-------------------------------|--------------------|-------|-------------------------------------|
| $2\sqrt{x}-3=0$ | Let $\sqrt{x}=t$, then $2t-3=0$ | $t=\frac{3}{2}$ | $t=\frac{3}{2}>0$ | $\sqrt{x}=\frac{3}{2}$, so $x=\frac{9}{4}$ |
| $x-2\sqrt{x}+1=0$ | | | | |
| $x+2+\sqrt{x+2}=0$ | | | | |

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