
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
There are three bags labeled $A$, $B$, and $C$. Bag $A$ contains $1$ red ball, bag $B$ contains $2$ different white balls, and bag $C$ contains $3$ different yellow balls. Two balls are drawn from these bags.

$(1)$ How many ways are there to draw two balls of different colors?

$(2)$ How many ways are there to draw two balls of the same color?

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