
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
Let \(Q\) be a point inside triangle \(DEF\). Let \(H_1\), \(H_2\), and \(H_3\) be the centroids of triangles \(QEF\), \(QFD\), and \(QDE\) respectively. If the area of triangle \(DEF\) is 24, then find the area of triangle \(H_1 H_2 H_3\).

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