
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 ten distinguishable rings, let $n$ be the number of possible six-ring arrangements on all five fingers of one hand. The order of rings on each finger is significant, and each finger must have at least one ring. Calculate the first three leftmost nonzero digits of $n$.

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