
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 box, there are $10$ small balls of the same size and shape, including $3$ black balls and $7$ white balls. Now, three people randomly take one ball each from the box in turn. After the first person takes out a ball, records its color, and puts it back into the box, the next person takes a ball. Calculate the probability that exactly one of these three people will draw a black ball.

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