
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 in triangle ABC, side AB measures 4 units and side AC measures 5 units, and the angle ∠BAC is 60°, and in another triangle ADE, AD = 2.5 units, and ∠DAE = 60°, and the areas of both triangles are equal, calculate the length of side AE.

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