
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 drawer in a darkened room contains $150$ red socks, $120$ green socks, $100$ blue socks, $80$ purple socks, and $50$ orange socks. A person selects socks one at a time from the drawer but cannot see the color of the socks being drawn. What is the smallest number of socks that must be selected to guarantee that the selection contains at least $15$ pairs of socks?

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