
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 $f(x) = ax - x^3$, for any $x_1, x_2$ in the interval $(0, 1)$, and $x_1 < x_2$, find the range of the real number $a$ such that $f(x_2) - f(x_1) > x_2 - x_1$ always holds.

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