
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
A student was determining the interval $D$ where the root $x_0$ of the equation $x^3 = -x + 1$ lies. They set the function $f(x) = x^3 + x - 1$, calculated $f(-1) < 0$, and $f(1) > 0$. In the process, they used the "bisection method" and chose 3 more values, which are $x_1$, $x_2$, $x_3$, to finally determine the interval $D$. What is the interval $D$?

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