
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 $P(n)$ represent the product of all non-zero digits of a positive integer $n$. For example: $P(123) = 1 \times 2 \times 3 = 6$ and $P(206) = 2 \times 6 = 12$. Find the value of $P(1) + P(2) + \cdots + P(999)$.

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