
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
Read the following solution process and then answer questions (1), (2), (3).  
Example: Solve the absolute value equation: $|2x|=1$.  
Solution: Discussion:  
① When $x\geqslant 0$, the original equation can be simplified to $2x=1$, and its solution is $x=\frac{1}{2}$.  
② When $x \lt 0$, the original equation can be simplified to $-2x=1$, and its solution is $x=-\frac{1}{2}$.  
Therefore, the solution to the original equation is $x=\frac{1}{2}$ and $-\frac{1}{2}$.  
Question (1): Following the solution method in the example, the solution to the equation $|\frac{1}{2}x|=2$ is ______;  
Question (2): Try to solve the absolute value equation: $2|x-2|=6$;  
Question (3): Based on understanding the solution to absolute value equations, solve the equation: $|x-2|+|x-1|=5$.

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