
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
Forty-four trainees have been captured by the evil François who, in his great kindness, gives them a chance to escape his trap. He makes them enter one by one into a large room that contains 44 drawers, each containing the name of a trainee (the names are assumed to be distinct). If the trainee finds his or her own name by opening fewer than 22 drawers, they move to another room to wait for their friends. Otherwise, François kills everyone. Find a strategy that gives the trainees at least a $30 \%$ chance of survival.

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