
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
How many integers $N$ less than $2000$ can be written as the sum of $j$ consecutive positive odd integers for exactly 6 different values of $j \ge 1$?

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