
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 large drawer contains a combination of red socks and green socks, at most $3000$ in total. It is noted that when two socks are selected randomly without replacement, the probability that both are red or both are green is exactly $\frac{3}{5}$. Determine the largest possible number of red socks in the drawer consistent with this information.

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