
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
"The Nine Chapters on the Mathematical Art" is an outstanding representation of ancient Chinese mathematical achievements. Among them, the "Rectangular Fields" chapter provides an empirical formula for calculating the area of a circular segment: area of the circular segment = $\frac{1}{2}$ (chord × sagitta + sagitta$^2$). A circular segment is formed by a circular arc and its corresponding chord. In the formula, "chord" refers to the length of the chord of the circular arc, and "sagitta" is the difference between the radius and the distance from the center of the circle to the chord. According to this empirical formula, there is a discrepancy between the calculated area of the circular segment and its actual area. Given a circular segment with a central angle of $\frac{2}{3}\pi$ and a chord length of 9 meters, the difference between the area of the circular segment calculated using the empirical formula from "The Nine Chapters on the Mathematical Art" and its actual area is ______.

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