
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 ${a_{n+1}=\begin{cases}2{a_n},0\leqslant {a_n}\leqslant \frac{1}{2} \\ 2{a_n}-1, \frac{1}{2} < {a_n}\leqslant 1\end{cases}}$, with the initial term $a_1=\frac{3}{5}$. Determine the value of $a_{2014}$.

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