
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]


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Isosceles triangle $PQR$ with an area of 144 square inches is cut by line segment $ST$ into an isosceles trapezoid and a smaller isosceles triangle. The area of the trapezoid is 108 square inches. If the altitude of triangle $PQR$ from $P$ is 24 inches, determine the length of segment $ST$.

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