
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 mathematics competition committee is composed of 9 professors. The finalized exam questions are stored in a safe that requires at least 6 professors to be present to open it. How many locks should be installed on the safe at a minimum, how many keys are needed, and how should the keys be distributed to the committee members?

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