
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 red, blue, and green socks, at most $2500$ in all. It so happens that, when two socks are selected randomly without replacement, there is a probability of exactly $\frac{2}{3}$ that both socks have the same color. 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