
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
A rectangular prism has three distinct faces of area  $24$ ,  $30$ , and  $32$ . The diagonals of each distinct face of the prism form sides of a triangle. What is the triangle’s area?

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