
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
There are  $11$  members in the competetion committee. The problem set is kept in a safe having several locks. 
The committee members have been provided with keys in such a way that every six members can open the safe, but no five members can do that.
What is the smallest possible number of locks, and how many keys are needed in that case?

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