
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
Given that the drawer contains  $100$  red socks,  $80$  green socks,  $60$  blue socks and  $40$  black socks, determine the smallest number of socks that must be selected to guarantee that the selection contains at least  $10$  pairs.

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