
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
Give an example of random variables $\xi_{n}$, for $n \geqslant 1$, such that

$$
\mathrm{E} \sum_{n=1}^{\infty} \xi_{n} \neq \sum_{n=1}^{\infty} \mathrm{E} \xi_{n}
$$

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