
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  $S(N)$  be the number of 1's in the binary representation of an integer  $N$ , and let  $D(N) = S(N + 1) - S(N)$ .  Compute the sum of  $D(N)$  over all  $N$  such that  $1 \le N \le 2017$  and  $D(N) < 0$ .

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