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A few-shot prompt can be used to guide a Large Language Model through a mathematical reasoning task by providing several demonstrations that establish a pattern. For instance, to teach a model to sum two numbers and divide by their product, the following examples could be used:

**DEMO**
* $${}12\ \ 5 \rightarrow (12 + 5)/(12 \times 5) = 0.283$$
* $${}3\ \ 1 \rightarrow (3 + 1)/(3 \times 1) = 1.33$$
* $${}-9\ \ 4 \rightarrow (-9 + 4)/(-9 \times 4) = 0.138$$
* $${}15\ \ 15 \rightarrow (15 + 15)/(15 \times 15) = 0.133$$

**USER**
* $${}19\ \ 73 \rightarrow$$

This structure allows the model to infer the required operation for the new input pair.

Example of a Few-Shot Prompt for a Mathematical Reasoning Task

You need to teach a language model to perform a specific two-step calculation: first, find the product of two numbers, and second, subtract the sum of those two numbers doubled from that product. Construct a complete few-shot prompt with at least three distinct demonstration examples that would guide the model to correctly solve for the input pair `10, 8`.

Constructing a Few-Shot Prompt for a Novel Calculation

Analyze the following scenario where an AI assistant produces an unexpected result for a mathematical task. Identify which of the provided demonstrations is the most likely cause of the error and explain your reasoning.

Debugging an AI's Mathematical Reasoning

A language model is given the following set of demonstrations to establish a pattern for a numerical task:

*   `2, 4 -> 9`
*   `10, 6 -> 64`
*   `5, 5 -> 25`

Based on the pattern demonstrated, what should the output be for the input `8, 12`?

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