
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 population of 1000 individuals numbered from 0, 1, 2, …, 999, they are divided into 10 groups sequentially, with group numbers from 0, 1, 2, …, 9. To draw a sample of size 10 using systematic sampling, it is stipulated that if the number x is randomly drawn from group 0, then the number drawn from group k will have its last two digits as the last two digits of $x + 33k$. When $x=24$, the 10 numbers drawn in the sample are __________. If among the 10 numbers drawn in the sample, one has its last two digits as 87, then the set of possible values for $x$ is __________.

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