
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 right circular cylinder has a height of $8$ and a radius of $5$. It is fully painted red. Two points, $A$ and $B$, are placed on the circumference of the top face such that $\overarc{AB}$ measures $90^\text{o}$. A plane is passed through $A$, $B$, and the cylinder's axis, slicing the cylinder into two halves and revealing a new unpainted face on each half. Calculate the area of one of these faces.

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