
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 that the function $f(x) = ax^3 + bx^2 + cx$ is increasing in the interval $[0,1]$ and decreasing in the intervals $(-\infty, 0)$ and $(1, +\infty)$, and also that $f'( \frac {1}{2}) = \frac {3}{2}$.
(Ⅰ) Determine the explicit formula for $f(x)$.
(Ⅱ) If it always holds that $f(x) \leqslant x$ in the interval $[0, m]$ where $m > 0$, find the range of $m$.

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