
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
In isosceles triangle $XYZ$, the area is 144 square inches. A line $\overline{MN}$ parallel to the base $XZ$ divides the triangle into two parts: an isosceles trapezoid and a smaller isosceles triangle $MNY$ at the top. The area of the smaller triangle $MNY$ is 36 square inches. If the altitude of the triangle $XYZ$ from $X$ is 24 inches, find the length of $\overline{MN}$.

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