
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
Place 6 identical small balls (where there are 2 red, 2 yellow, and 2 blue balls) randomly into 3 boxes, each with exactly 2 balls. Let $\xi$ be the number of boxes containing balls of the same color. Find the distribution of $\xi$.

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