
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
After reading the "problem" and "hint" below, complete the process of solving the equation and find the value of $x$.  
【Problem】Solve the equation: $x^{2}+2x+4\sqrt{{x^2}+2x}-5=0$.  
【Hint】You can solve the equation using the "substitution method".  
Solution: Let $\sqrt{{x^2}+2x}=t\left(t\geqslant 0\right)$, then we have $x^{2}+2x=t^{2}$, and the original equation can be transformed into: $t^{2}+4t-5=0$.  
$(1)$ Continue solving:  
$(2)$ Solve the equation using the above method: $\frac{{{x^2}}}{{x+2}}+\frac{{2x+4}}{{{x^2}}}=3$.

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