
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 triangle and a trapezoid have equal areas and share the same altitude. If the base of the triangle is 24 inches, and the base of the trapezoid is halved in length compared to the triangle, determine the length of the median of the trapezoid.

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