
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
Given the function $f(x) = \begin{cases} 1, & x\geq 0 \\ -2, & x<0 \end{cases}$, if $x_1$ and $x_2$ both satisfy the inequality $x+(x-1)f(x+1)\leq 5$, then the maximum value of $x_1-x_2$ is \_\_\_\_\_\_.

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