
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
The commission consists of 11 people. The materials that the commission is working on are kept in a safe. How many locks should the safe have and how many keys should each member of the commission be provided with so that access to the safe is possible when the majority of the members of the commission gather, but not possible if only less than half of the members gather?

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