
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 box, there are May beetles, consisting of $n$ males and $m$ females. Mr. Entomologist removes the beetles from the box in random order one by one, without returning them, until he has $k$ males, where $1 \leqslant k \leqslant n$. Let $x_{k}$ be the total number of beetles he has removed from the box. Find the probability that $x_{k}=x$, where $x=k, k+1, \ldots, k+m$, and determine the expected value of $x_{k}$.

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