
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
The new dormitory manager received 10 keys to open 10 rooms. He knows that each key can only open one of the rooms, but he does not know which key opens which room. Now, to open all the locked rooms, he needs to try at most     times.

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