
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 indoor football field is being designed with a length of $100 \text{m}$ and a width of $80 \text{m}$. The field must be illuminated by four spotlights, each hanging at some point on the ceiling. Each spotlight illuminates a circle with a radius equal to the height at which the spotlight is hanging. Determine the minimum possible ceiling height such that the following conditions are met: every point on the football field is illuminated by at least one spotlight; the ceiling height must be a multiple of $0.1 \text{m}$ (e.g., $19.2 \text{m}$, $28 \text{m}$, $33.9 \text{m}$, etc.).

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