
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 interns have been captured by the evil François who, in his great kindness, gives them a chance to escape from his trap. He makes them enter one by one into a large room containing 44 drawers, each with the name of an intern (the names are assumed to be unique). If an intern finds their name in fewer than 22 drawers, they move to another room to wait for their friends. Otherwise, François kills everyone. Find a strategy that gives the interns at least a $30\%$ chance of survival.

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