
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
Given that \( AC \perp CE \), \( D \) is the midpoint of \( CE \), \( B \) is the midpoint of \( AC \). Connect \( AD \) and \( EB \), and let \( AD \) and \( EB \) intersect at \( F \). If \( BC = CD = 15 \), find the area of \(\triangle DEF\).

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