
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
The sequence $\{a_n\}$ satisfies $a_{n+1}= \begin{cases}2a_{n} & (0\leqslant a_{n} < \frac {1}{2}) \\ 2a_{n}-1 & ( \frac {1}{2}\leqslant a_{n} < 1).\end{cases}$ and $a_{1}= \frac {6}{7}$, then $a_{20}=$ ______.

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