
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 a bag, there are $4$ white balls and $2$ black balls. Three balls are randomly drawn from the bag consecutively, one at a time.<br/>$(Ⅰ)$ If the balls are not replaced after each draw, find the probability of drawing at least one black ball in the three draws;<br/>$(Ⅱ)$ If the balls are replaced after each draw, find the probability of drawing exactly one black ball in the three draws.

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