
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 the recursive relation: 
$$
a_{n+1}= 
\begin{cases} 
2a_{n} & (0 \leqslant a_{n} < \frac {1}{2}) \\
2a_{n}-1 & (\frac {1}{2} \leqslant a_{n} < 1)
\end{cases}
$$
with the initial condition $a_{1}= \frac {6}{7}$, calculate the value of $a_{2012}$.

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