
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 socks and blue socks, at most $2500$ in all. When two socks are selected randomly without replacement, the probability that both are red or both are blue is $\frac{3}{5}$. Additionally, it is known that there are more red socks than blue socks. What is the largest possible number of red socks in the drawer that meets these conditions?

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