
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 $f(x)=-x^{3}+ax$, where $a\in\mathbb{R}$, and $g(x)=- \frac {1}{2}x^{ \frac {3}{2}}$,

$(1)$ Determine the monotonicity of the function $f(x)$;

$(2)$ If $f(x) < g(x)$ holds true on the interval $(0,1]$, find the range of the real number $a$.

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