
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
For each positive integer  $n$ , let  $g(n)$  be the sum of the digits when  $n$  is written in binary.  For how many positive integers  $n$ , where  $1\leq n\leq 2007$ , is  $g(n)\geq 3$ ?

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