
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
It is known that there is 1 red ball and 5 white balls in box $A$, and there are 3 white balls in box $B$. Now, 3 balls are randomly taken out from box $A$ and placed in box $B$. After thorough mixing, 3 balls are randomly taken out from box $B$ and placed in box $A$. What is the probability that the red ball was transferred from box $A$ to box $B$ and then returned to box $A$?

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