
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
Let \( \star (x) \) denote the sum of the digits of a positive integer \( x \). Define \( \mathcal{S} \) as the set of positive integers where for all elements \( n \) in \( \mathcal{S} \), \( \star (n) = 15 \) and \( 100 \le n < 10^{5} \). Compute \( \star(m) \), where \( m \) is the number of elements in \( \mathcal{S} \).

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