
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 every $\varepsilon > 0$, there exists a number $k$ such that for all $n > k$, $\left|x_{n} - a\right| \geqslant \varepsilon$.

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