
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 {x} denote the fractional part of x = x - [x]. The sequences \( x_1, x_2, x_3, \ldots \) and \( y_1, y_2, y_3, \ldots \) are such that \( \lim \{ x_n \} = \lim \{ y_n \} = 0 \). Is it true that \( \lim \{ x_n + y_n \} = 0 \)? \( \lim \{ x_n - y_n \} = 0 \)?

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