
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 $a\_n= \begin{cases} n,&n\text{ is odd} \\ a\_{\frac{n}{2}},&n\text{ is even} \end{cases}$, let $S\_n$ be the sum of the first $n$ terms of the sequence. Calculate the value of $S\;_{2^{2016}-1}$.

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