
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
\[ f(x) = \frac{x(1-x)}{x^3 - x + 1} \quad (0 < x < 1) \]
If the maximum value of \( f(x) \) occurs at \( f(x_0) \), then \( x_0 = \) $\qquad$ .

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