
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 point \( O \) be the origin in a three-dimensional coordinate system, and let points \( A, \) \( B, \) and \( C \) be located on the positive \( x, \) \( y, \) and \( z \) axes, respectively. If \( OA = \sqrt[4]{81} \) and \( \angle BAC = 45^\circ, \) compute the area of triangle \( ABC. \)

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