
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) = $$\begin{cases} x^{2}-3tx+18，x≤3 \\ (t-13) \sqrt {x-3}，x＞3\end{cases}$$, let a<sub>n</sub> = f(n) (n∈N*), if {a<sub>n</sub>} is a decreasing sequence, then the range of the real number t is _____.

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