
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
In the sequence $\{a_{n}\}$, ${a}_{n+1}=\left\{\begin{array}{c}2{a}_{n},{a}_{n}＜\frac{1}{2}\\ 2{a}_{n}-1,{a}_{n}≥\frac{1}{2}\end{array}\right.$, if ${a}_{1}=\frac{4}{5}$, then the value of $a_{2023}$ is ______.

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