
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
Let $g(n)$ denote the largest odd factor of the natural number $n$. For example, the factors of $9$ are $1$, $3$, $9$, so $g(9)=9$; the factors of $10$ are $1$, $2$, $5$, $10$, so $g(10)=5$. Find the value of $g(1)+g(2)+g(3)+…+g(2^{2016}-1)$.

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