
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
Given a hexadecimal number composed of digits from $0$ to $9$ and the letters $\mathrm{A}$ to $\mathrm{F}$, where $\mathrm{A}, \mathrm{B}, \cdots, \mathrm{F}$ correspond to $10, 11, \cdots, 15$, determine the total count $n$ of hexadecimal numbers that use only digits within the first 1000 positive integers. Find the sum of the digits of $n$.

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