
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
From a group of $1003$ students, $50$ representatives are to be selected. First, $3$ students are eliminated through simple random sampling. Then, the remaining $1000$ students are evenly divided into $20$ groups. Using systematic sampling, $50$ students are selected. Calculate the probability that each student is selected.

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