
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 $OA = \sqrt[3]{50}$ and $\angle BAC = 45^\circ$, compute the area of triangle $ABC$.

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