
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 ${a_n} = -n + t$ and the general term formula of the sequence ${b_n} = {2^n}$, the sequence ${c_n}$ satisfies ${c_n} = \frac{{{a_n} + {b_n}}}{2} + \frac{{\left| {{a_n} - {b_n}} \right|}}{2}$. It is also known that ${c_n} \geqslant {c_3}(n \in {N^*})$, find the range of values of the real number $t$.

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