
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 $f(x) = |x - 1|$, if there exist $x_1, x_2 \in [a, b]$ and $x_1 < x_2$ such that $f(x_1) \geq f(x_2)$ holds, describe the real numbers $a$ and $b$.

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