
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
Does there exist a positive integer  $n{}$  such that for any real  $x{}$  and  $y{}$  there exist real numbers  $a_1, \ldots , a_n$  satisfying \[x=a_1+\cdots+a_n\text{ and }y=\frac{1}{a_1}+\cdots+\frac{1}{a_n}?\]
*Artemiy Sokolov*

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