
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
Given 2006 students, 50 are to be selected to form a visiting group. If the selection is made by first using simple random sampling to eliminate 6 students from the 2006, and then randomly selecting 50 from the remaining 2000 students, calculate the respective probabilities of a specific student being eliminated and being selected.

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