
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
Qin Jiushao, a famous mathematician from the Southern Song dynasty in China, discovered a formula for calculating the area of a triangle from its three sides. He referred to this method as "three oblique sides area calculation." In chapter five of the "Field Categories" section in his work "Mathematical Book in Nine Chapters," there is a question that asks, "Suppose there is a triangular field with three oblique sides: the smallest is 14 zhang, the medium is 24 zhang, and the largest is 25 zhang. How much is the area of the field?" (Mathematical Book in Nine Chapters) The method provided is: "Take the square of the smallest oblique side added to the square of the largest oblique side minus the square of the medium oblique side, halve the remainder, square it, subtract from the product of the square of the smallest oblique side and the square of the largest oblique side, divide the remainder by four, use this as a fact, take the square root and get the area." Please answer the area of the triangular field (whose sides measure 14 zhang, 24 zhang, and 25 zhang respectively) in square zhang. (Note: Here, 'oblique' refers to the side length; the smallest oblique side is the shortest side, and 'square' refers to the squared value.)

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