
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
Let \(ABCD\) be a square and \(X\) and \(Y\) be points such that the lengths of \(XY\), \(AX\), and \(AY\) are 6, 8, and 10 respectively. The area of \(ABCD\) can be expressed as \(\frac{m}{n}\) square units where \(m\) and \(n\) are positive integers without common factors. Find the value of \(m+n\).

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