
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
A positive integer will be called "sparkly" if its smallest positive divisor, other than 1, equals the total number of divisors (including 1). How many of the numbers \(2, 3, \ldots, 2003\) are sparkly?

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