
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
The organizer of a conference invited five experts, A, B, C, D, and E, to attend an academic conference and arranged their seats. If the five experts randomly choose a seat to sit in and happen to sit in the seat arranged by the organizer, it is considered a correct seat; otherwise, it is considered an incorrect seat. Let $X$ be the number of experts sitting in the correct seat. Find the distribution table and the expected value of the random variable $X$; (2) Given that three experts are sitting in the wrong seats, find the probability that exactly two experts are sitting in the correct seats.

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