
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 sequence $\{a_n\}$ with the general term $a_n = -n + t$, and the sequence $\{b_n\}$ with the general term $b_n = 3^{n-3}$, let $c_n = \frac{a_n + b_n}{2} + \frac{|a_n - b_n|}{2}$. In the sequence $\{c_n\}$, if $c_n \geqslant c_3$ for $n \in \mathbb{N}^*$, then the range of the real number $t$ is ______.

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