
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
10 guests arrived and each left a pair of galoshes in the hallway. Each pair of galoshes is of a different size. The guests began to leave one by one, putting on any pair of galoshes that they could fit into (i.e., each guest could put on a pair of galoshes that is not smaller than their own size). At some point, it was found that none of the remaining guests could find a pair of galoshes to leave. What is the maximum number of guests that could be left?

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