
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
In box A, there are 3 balls of each of the following colors: red, black, and white. In box B, there are 2 balls of each of the following colors: yellow, black, and white. One ball is drawn from each box.

\\((1)\\) Calculate the probability that the two balls drawn are of different colors;

\\((2)\\) Please design a method of random simulation to approximate the probability of drawing two balls of different colors as calculated in \\((1)\\). Write out the steps of the simulation.

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