
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
Let \( n \) be a natural number. Indicate the smallest intervals on the number line that contain the first 100 points of the following sequences:
1) \( x = \frac{(-1)^n}{n} \);
2) \( y = 1 - \frac{1}{n} \);
3) \( z = |n-50| \);
4) \( t = (-0.5)^n \).

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