
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
(1) When the value of $|x-2|+|x-3|$ is minimized, the maximum and minimum values of $|x-3|-|x-2|+|x-1|$ are respectively.  
(2) Given positive integers $a$ and $b$ satisfying $|b-2|+b-2=0$ and $|a-b|+a-b=0$, find the value of $ab$.

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