
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
For two functions $m(x)$ and $n(x)$ that are defined on the interval $[a, b]$, if for any $x$ within the interval $[a, b]$, it holds that $|m(x) - n(x)| \leq 1$, then $m(x)$ and $n(x)$ are said to be "close functions" on $[a, b]$, and the interval $[a, b]$ is called a "close interval". If the function $m(x)=x^2-3x+4$ and $n(x)=2x-3$ are close functions on the interval $[a, b]$, then the maximum value of $b - a$ is______.

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