
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
In a sequence of four connected 30-60-90 triangles, the hypotenuse of each triangle serves as the longer leg of the adjacent smaller triangle. The hypotenuse of the largest triangle is 10 centimeters. Determine the length of the longer leg of the smallest triangle.

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