
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
Inside a rectangle with a width of 8 and a length of 12, two congruent equilateral triangles are drawn such that they share one side, and each has one vertex touching a short side of the rectangle. What is the area of the largest rectangle that can be inscribed between the triangles and within the original rectangle?

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