
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 ${a_{n}}$, $a_{n+1}=\begin{cases} 2a_{n}\left(a_{n} < \frac{1}{2}\right) \\ 2a_{n}-1\left(a_{n}\geqslant \frac{1}{2}\right) \end{cases}$, if $a_{1}=\frac{4}{5}$, then the value of $a_{20}$ is $\_\_\_\_\_\_$.

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