
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 mix of green socks and yellow socks, at most 2500 in all. It turns out that when two socks are chosen randomly without replacement, there is a probability of exactly $\frac{2}{3}$ that both are green or both are yellow. Determine the largest possible number of green socks in the drawer that is consistent with this data.

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