
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 $f(x)= \begin{cases} 3^{x}, & x\in[0,1] \\ \frac {9}{2}- \frac {3}{2}x, & x\in(1,3]\end{cases}$, when $t\in[0,1]$, $f(f(t))\in[0,1]$, then the range of the real number $t$ is ______.

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