
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
Rectangle \( ABCD \) has \( AB = 10 \) and \( BC = 8 \). Point \( M \) is the midpoint of diagonal \( \overline{AC} \), and \( E \) is on \( AB \) such that \( \overline{ME} \perp \overline{AC} \). Calculate the area of \( \triangle AME \).
A) \( \frac{85}{8} \)  
B) \( \frac{104}{8} \)  
C) \( \frac{106}{8} \)  
D) \( \frac{97}{8} \)  
E) \( \frac{93}{8} \)

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