
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
Each triangle in a sequence is either a 30-60-90 triangle or a 45-45-90 triangle. The hypotenuse of each 30-60-90 triangle serves as the longer leg of the adjacent 30-60-90 triangle, except for the final triangle which is a 45-45-90 triangle. The hypotenuse of the largest triangle is 16 centimeters. What is the length of the leg of the last 45-45-90 triangle? Express your answer as a common fraction.

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