
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, vertices A, B, and C are positioned such that AB = 4.5 meters, AC = 5 meters, and the angle at vertex A (angle BAC) is 30 degrees. There is a smaller triangle ADE inside triangle ABC sharing vertex A and the side AD is parallel to BC. If the length AD is 1.5 meters, find the length of side AE.
A) 1.2 meters
B) 1.6667 meters
C) 2.25 meters
D) 3 meters

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