
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 $t>0$, the function $f(x) = \begin{cases} x(x-t)^{2}, & x\leq t \\ \frac{1}{4}x, & x>t\end{cases}$, if the function $g(x) = f(f(x)-1)$ has exactly 6 distinct zeros, then the range of the real number $t$ is \_\_\_\_\_\_.

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