
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
Provide an example of a function that is equal to zero for any values of \( x \) that are equal to any of the numbers \( a_{1}, a_{2}, a_{3}, \ldots, a_{n} \), and as \( x \) approaches any of the numbers \( b_{1}, b_{2}, b_{3}, \ldots, b_{n} \), grows beyond all bounds (evidently, all numbers \( b \) are different from all numbers \( a \)).

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