
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 dresser contains a mix of red, blue, and yellow socks, with a maximum of 2300 socks in total. When three socks are selected randomly without replacement, there is a probability exactly equal to $\frac{1}{3}$ that all three are of the same color. What is the largest possible number of red socks that can be in the dresser, given these conditions?

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