
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
In a box, there are red and black socks. If two socks are randomly taken from the box, the probability that both of them are red is $1/2$.

a) What is the minimum number of socks that can be in the box?

b) What is the minimum number of socks that can be in the box, given that the number of black socks is even?

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