
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 contains a mixture of red, blue, and white socks, with at most 2025 socks in total. When two socks are selected randomly without replacement, there is a probability of exactly $\frac{1}{3}$ that both socks are of the same color (either both red, both blue, or both white). What is the largest possible number of red socks in the drawer that is consistent with this data?

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