
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 a sequence \(\{a_n\}\) that satisfies \(a_{n+1}=\begin{cases}2a_{n} (0 \leqslant a_{n} < \frac {1}{2})\\2a_{n}-1 (\frac {1}{2} \leqslant a_{n} < 1)\end{cases}\), if \(a_{1}=\frac {6}{7}\), calculate the value of \(a_{2011}\).

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