
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 point \( Q \) is chosen in the interior of \(\triangle DEF\) such that when lines are drawn through \( Q \) parallel to the sides of \(\triangle DEF\), the resulting smaller triangles \( t_{4} \), \( t_{5} \), and \( t_{6} \) have areas \( 16 \), \( 25 \), and \( 36 \) respectively. Calculate the area of \(\triangle DEF\).

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