
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
Ingots of highly enriched uranium need to be stored in such a manner that the distance to the nearest ingot is as large as possible. If there are several suitable locations, any one of them can be chosen. Unfortunately, no one knows how many ingots will need to be stored. Ingots arrive one by one, and once placed in storage, they cannot be moved.

An empty warehouse complex has 81 storage rooms arranged in a single row. The first arriving ingot is placed in room 1, and the second, according to recommendations, in room 81.

In which rooms might the 6th arriving ingot be placed? Indicate all possible options for the answer.

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