
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
Associate with an $x$ less than 1 a number $y$ greater than 1—if it exists—for which the following equation holds:

$$
\int_{x} \frac{1}{u^{2}} d u = \int_{1}^{y} \frac{1}{u^{2}} d u
$$

What are the domain and range of this function? What is the right-hand limit of the function as the argument approaches the left endpoint of the domain?

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