
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 way that the distance to the nearest ingot is as large as possible. If there are several suitable locations, any of them can be chosen. Unfortunately, nobody knows how many ingots will need to be stored. Ingots arrive one by one. Once placed in storage, an ingot cannot be moved.

An empty storage complex has 161 storage rooms arranged in a single row. The first arriving ingot is placed in room 1, and the second, according to recommendations, is placed in room 161.

In which rooms can the 6th arriving ingot be placed? List all possible answers.

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