
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
Currently, there are 50 drivers and 40 cars, with each car having a unique lock. In order to ensure that any 40 out of the 50 drivers can go to work with the 40 cars operational, assuming all keys are in the drivers' possession, at least how many keys are needed?

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