
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 $f(x) = |\ln(x - 1)|$, if there exist $x_1, x_2 \in [a, b]$ such that $x_1 < x_2$, and $f(x_1) > f(x_2)$, determine the correct description of the real numbers $a$ and $b$.

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