
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 diagonal \(BD\) with endpoints \(B(4,2)\) and \(D(12,8)\). Diagonal \(AC\) lies on the line with equation \(x + 2y - 18 = 0\). Determine the area of \(ABCD\).

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