
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 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 \(ED\) if it is known that \(AE = 15\) and \(AC = 12\).

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