
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
A trapezoid has side lengths 4, 6, 8, and 10. The trapezoid can be rearranged to form different configurations with sides 4 and 8 as the parallel bases. Calculate the total possible area of the trapezoid with its different configurations.
A) $24\sqrt{2}$
B) $36\sqrt{2}$
C) $42\sqrt{2}$
D) $48\sqrt{2}$
E) $54\sqrt{2}$

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