
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
A toy consists of 9 differently sized rings and a tapering pole. All the rings can only be stacked on the pole in a single way at once (by placing the largest at the bottom, followed by the others in decreasing order of size), as each ring gets stuck at its respective position. Until we reach the top of the pole, we can place the rings in any order: even the largest does not pass through even the smallest.

How many different configurations can be created, considering the arrangements where the pole’s top is not reached?

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