
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
7 scientists are engaged in a confidential technical research. Their laboratory is equipped with an "electronic lock," and each participant in this work has a key to open the electronic lock. For safety reasons, at least 4 scientists must be present to open the laboratory door. How many characteristics must this "electronic lock" possess? How many of these characteristics should each scientist's key have?

This is purely a quantitative study rather than a concrete design of such a "lock" and "key". For easier understanding, consider the problem as determining how many locks should be on the door, and how many keys each scientist should carry.

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