
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
Analogy and transformation are the most commonly used mathematical thinking methods in solving new problems in mathematics.  
[Reviewing old knowledge, solving by analogy]  
Solve the equation: $\sqrt{x+1}=2$.  
Solution: Taking the square of both sides, we get a linear equation ____, solving this equation, we get $x=____$.  
After verification, $x=$____ is a solution to the original equation.  
[Learning transformation, solving problems]  
Apply the above method to solve the following equations:  
$(1) \sqrt{x-2}-3=0$;  
$(2) \sqrt{4{x^2}+5x}-2x=1$.

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