
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 $\star (x)$ be the sum of the digits of a positive integer $x$. Define $\mathcal{S}$ as the set of all positive integers such that for each element $n$ in $\mathcal{S}$, $\star (n)=16$ and $0 \le n < 10^{8}$. If $m$ represents the number of elements in $\mathcal{S}$, compute $\star(m)$.

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