
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 the interior of a triangle \( ABC \) with area 1, points \( D \), \( E \), and \( F \) are chosen such that \( D \) is the midpoint of \( AE \), \( E \) is the midpoint of \( BF \), and \( F \) is the midpoint of \( CD \). Find the area of triangle \( DEF \).

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