
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
Ashwin the frog is traveling on the $xy$-plane in a series of $2^{2017}-1$ steps, starting at the origin. At the $n^{\text{th}}$ step, if $n$ is odd, Ashwin jumps one unit to the right. If $n$ is even, Ashwin jumps $m$ units up, where $m$ is the greatest integer such that $2^{m}$ divides $n$. If Ashwin begins at the origin, what is the area of the polygon bounded by Ashwin's path, the line $x=2^{2016}$, and the $x$-axis?

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