
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 triangle $DEF$, $DE = 8$, $EF = 6$, and $FD = 10$.

[asy]
defaultpen(1);

pair D=(0,0), E=(0,6), F=(8,0);
draw(D--E--F--cycle);

label("\(D\)",D,SW);
label("\(E\)",E,N);
label("\(F\)",F,SE);

[/asy]

Point $Q$ is arbitrarily placed inside triangle $DEF$. What is the probability that $Q$ lies closer to $D$ than to either $E$ or $F$?

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