
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 $f(x) = ||x - 1| - 1|$, if the equation $f(x) = m$ ($m \in \mathbb{R}$) has exactly four distinct real roots $x_1, x_2, x_3, x_4$, then the range of values for $x_1x_2x_3x_4$ is.

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