
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 to 999, they are divided into 10 groups, with group numbers from 0 to 9. A systematic sampling method is to be used to draw a sample of size 10. It is stipulated that if a number $x$ is randomly drawn from group 0, then the numbers drawn from the subsequent groups are obtained by sequentially displacing such that the last two digits of the number drawn from group $k$ are the last two digits of $x + 33k$.
(1) When $x = 24$, write down the 10 numbers drawn from the sample.
(2) If one of the 10 numbers drawn from the sample has the last two digits as 87, determine the range of values for $x$.

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