
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 $n$ boxes numbered $1$, $2$, $\ldots$, $n$. The first box contains $2$ white balls and $1$ black ball, while the rest of the boxes each contain $1$ white ball and $1$ black ball. Now, a ball is randomly taken from the first box and placed into the second box, then a ball is randomly taken from the second box and placed into the third box, and so on. The probability of drawing a white ball from the second box is ____, and the probability of drawing a white ball from the $n$th box is ____.

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