
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 triangles is connected where each triangle is either a 30-60-90 triangle or a 45-45-90 triangle. The hypotenuse of one triangle becomes the longer leg of the next 30-60-90 triangle or the leg of the next 45-45-90 triangle. The hypotenuse of the largest 30-60-90 triangle is 16 centimeters. What is the length of the leg opposite the 45-degree angle of the smallest 45-45-90 triangle?

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