
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 dresser contains a mixture of red socks and blue socks, at most \(2500\) in all. It so happens that, when two socks are selected randomly without replacement, there is a probability a little higher than \(\frac{1}{2}\), precisely \(\frac{12}{23}\), that both are red or both are blue. What is the largest possible number of red socks in the dresser that is consistent with this data?

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