
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 ${a}_{n+1} = \begin{cases} 2{a}_{n}, & 0 \leqslant {a}_{n} < \frac{1}{2} \\ 2{a}_{n}-1, & \frac{1}{2} \leqslant {a}_{n} < 1 \end{cases}$, and $a_{1} = \frac{3}{5}$. Find ${a}_{2015}$.

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