
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
Let the function $f(x) = \begin{cases} 3^{x}, & x \in (-\infty, 1] \\ \frac{9}{2} - \frac{3x}{2}, & x \in (1, 3) \end{cases}$. Find $f(-\log_3 2)$ and if $f(f(t)) \in [0, 1]$, determine the range of the real number $t$.

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