
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 \( ABC \), the angle bisector \( AL \) is drawn. Points \( E \) and \( D \) are marked on segments \( AB \) and \( BL \), respectively, such that \( DL = LC \) and \( ED \parallel AC \). Find the length of segment \( ED \), given \( AE = 15 \) and \( AC = 12 \).

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