
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 general term formula of the sequence $\left\{a_{n}\right\}$ as $a_{n}=-n+t$, and the general term formula of the sequence $\left\{b_{n}\right\}$ as $b_{n}={3}^{n-3}$, define the sequence $\left\{c_{n}\right\}$ as $c_{n}= \frac{a_{n}+b_{n}}{2}+ \frac{\left|a_{n}-b_{n}\right|}{2}$. In the sequence $\left\{c_{n}\right\}$, if $c_{n}\geqslant c_{3}\left(n∈\mathbb{N}^{*}\right)$, then the range of the real number $t$ is _______.

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