
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
In each cell of a $1 \times N$ strip, there is either a plus or a minus. Vanya can perform the following operation: choose any three cells (not necessarily consecutive), one of which is exactly in the middle between the other two cells, and change the signs in these three cells to their opposites. We call the number $N$ positive if, starting from $N$ minuses, Vanya can obtain a sequence of $N$ pluses using these operations.

Consider the numbers $3, 4, 5, \ldots, 1400$. How many of them are positive?

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