
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
In how many ways can the number 10000 be factored into three natural factors, none of which is divisible by 10? Factors that differ only in the order of multiplication are considered the same.

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