
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
Two 30-60-90 triangles, each with a hypotenuse of 10 cm, are placed such that one vertex of each triangle exactly coincides while they lay flat on a surface. This configuration causes a new overlapping triangle region to form. Calculate the area of this overlapping region when the overlapping region forms another 30-60-90 triangle.
A) $\dfrac{45}{8} \text{ cm}^2$
B) $\dfrac{60}{8} \text{ cm}^2$
C) $\dfrac{75}{8} \text{ cm}^2$
D) $\dfrac{90}{8} \text{ cm}^2$

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