
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
Consider an isosceles triangle \( DEF \) where \( DE = EF = 5 \) and \( DF = 6 \). 

Point \( Q \) is randomly selected inside the triangle \( DEF \). What is the probability that \( Q \) is closer to vertex \( E \) than to vertex \( D \) or \( F \)?

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