
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 $f(x)= \begin{cases} x-x^{2},x\in[0,1] \\ - \frac { \sqrt {5}}{5}f(x-1),x\in[1,3]\end{cases}$,
(I) Find $f( \frac {5}{2})$ and the analytical expression of function $f(x)$ when $x\in[2,3]$.
(II) If $f(x)\leqslant \frac {k}{x}$ holds for any $x\in(0,3]$, find the minimum value of the real number $k$.

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