
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 method for finding the area of a triangle given the lengths of its three sides, as described in the "Nine Chapters on the Mathematical Art," filled a gap in traditional Chinese mathematics. This method is completely equivalent to Heron's formula, demonstrating the high level of mathematics in ancient China. The method is described as follows: "Subtract the square of the intermediate slant height from the sum of the squares of the smaller and larger slant heights, take half of the result, and multiply it by the slant height. Subtract the product of the smaller and larger slant heights from this, take the square root of the remainder, and the result is the area." If we express this in the form of a formula, we get: S = $$\sqrt { \frac{1}{4}[c^{2}a^{2}-( \frac {c^{2}+a^{2}-b^{2}}{2})^{2}]}$$. Given that triangle ABC satisfies (sinA - sinB)(sinA + sinB) = sinA sinC - sin²C and AB = 2BC = 2$$\sqrt {2}$$, use the given formula to find the area of triangle ABC.

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