
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 an opaque bag, there are four small balls labeled with the Chinese characters "阳", "过", "阳", and "康" respectively. Apart from the characters, the balls are indistinguishable. Before each draw, the balls are thoroughly mixed.<br/>$(1)$ If one ball is randomly drawn from the bag, the probability that the character on the ball is exactly "康" is ________; <br/>$(2)$ If two balls are drawn from the bag by person A, using a list or a tree diagram, find the probability $P$ that one ball has the character "阳" and the other ball has the character "康".

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