
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 five-ring arrangements on the four fingers (not the thumb) of one hand, with each finger having at least one ring. The order of rings on each finger is significant. Find the leftmost three nonzero digits of $n$.

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