
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
At a ball, $n$ married couples attend. In each couple, the husband and wife are of exactly the same height, but no two couples have the same height. When the waltz begins, everyone pairs up randomly: each gentleman dances with a randomly chosen lady. Find the expected value of the random variable $X$, which represents the number of gentlemen who are shorter than their partners.

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