
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
Given the formula $S=\sqrt{\frac{1}{4}\left[ c^{2}a^{2}-\left(\frac{c^{2}+a^{2}-b^{2}}{2}\right)^{2} \right]}$ for calculating the area of a triangle, where $a > b > c$, find the area of the triangle with smaller diagonal 13 li, middle diagonal 14 li, and larger diagonal 15 li.

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