
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
For each of the following sequences, indicate all its limit points:
a) \( x_{n} = \frac{n+1}{n} \),

b) \( x_{n} = (-1)^{n} \),

c) \( x_{n} = \sin n^{\circ} \),

d) \( x_{n} = n^{(-1)^{n}} \),

e) \( x_{n} = n \),

f) \( \frac{1}{2} ; \frac{1}{3} ; \frac{2}{3} ; \frac{1}{4} ; \frac{2}{4} ; \frac{3}{4} ; \frac{1}{5} ; \frac{2}{5} ; \frac{3}{5} ; \frac{4}{5} ; \ldots \)

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