
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 lines drawn through $Q$ parallel to the sides of $\triangle DEF$ form smaller triangles $u_{1}$, $u_{2}$, and $u_{3}$ inside $\triangle DEF$, with areas $16$, $25$, and $64$, respectively. Find the area of $\triangle DEF$.

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