
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 sequence of linked metallic rings, each 1 cm thick, are stacked vertically on a peg. The top ring's outer diameter is 22 cm. Each subsequent ring below has its outer diameter 2 cm less than the ring above it, and all rings have even-numbered outer diameters. The smallest possible diameter for any ring is 4 cm. Calculate the total vertical distance from the top of the uppermost ring to the bottom of the lowest ring.

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