
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
Find the number of positive integers  $k \le 2018$  for which there exist integers  $m$  and  $n$  so that  $k = 2^m + 2^n$ .
For example,  $64 = 2^5 + 2^5$ ,  $65 = 2^0 + 2^6$ , and  $66 = 2^1 + 2^6$ .

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