
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
Bag A contains 1 white ball, 2 red balls, and 3 black balls, all of the same size. Bag B contains 2 white balls, 3 red balls, and 1 black ball, also of the same size. If one ball is drawn from each bag, what is the probability that the two balls are of the same color?

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