
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
A locker at a crowded sports club contains 80 red socks, 70 yellow socks, 50 green socks, 60 blue socks, and 40 orange socks. A player selects socks one at a time from the locker without being able to see their color. What is the smallest number of socks that must be selected to guarantee that the selection contains at least 15 pairs?

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