System: You are a helpful and precise assistant in checking the quality of the answer.
User: We would like to request your feedback on the performance of the response of the assistant to the user instruction displayed below. In the feedback, I want you to rate the quality of the response in these 3 categories according to each scoring rubric:

Logical Robustness: Does the model ensure general applicability and avoid logical contradictions in its reasoning steps for an instruction that requires step-by-step logical process? This includes the consideration of edge cases for coding and mathematical problems, and the absence of any counterexamples.
Score 1: The logic of the model's response is completely incoherent.
Score 2: The model's response contains major logical inconsistencies or errors.
Score 3: The model's response contains some logical inconsistencies or errors, but they are not significant.
Score 4: The model's response is logically sound, but it does not consider some edge cases.
Score 5: The model's response is logically flawless and it takes into account all potential edge cases.
Logical Correctness: Is the final answer provided by the response logically accurate and correct for an instruction that has a deterministic answer?
Score 1: The model's final answer is completely incorrect and lacks sound reasoning.
Score 2: The model's final answer contains significant errors that critically undermine its correctness.
Score 3: The model's final answer includes inaccuracies that require considerable effort to correct.
Score 4: The model's final answer contains minor errors, which are easy to rectify and do not significantly impact its overall correctness.
Score 5: The model's final answer is completely accurate and sound.
Commonsense Understanding: Is the model accurately interpreting world concepts for instructions that require a simulation of the expected result or necessitate commonsense or spatial reasoning?
Score 1: The model completely misinterprets world concepts or misunderstands commonsense knowledge.
Score 2: The model misinterprets crucial world concepts, potentially leading to misinformation.
Score 3: The model shows a few errors in its understanding of world concepts.
Score 4: A single, minor error exists in the model's comprehension of world concepts.
Score 5: The model accurately interprets world concepts without any errors.
[Instruction]
There is a basket of no more than 5266771 oranges. If we divide them equally among 109 elephants, we have 8 left; if we divide them equally among 211 monkeys, we have 70 left; if we divide them equally among 229 racoons, we have 28 left. How many oranges are in the basket?

[Ground truth Answer]
2400406

[Assistant's Response]
To find the number of oranges in the basket, we can set up a system of congruences based on the information provided:

1. When divided by 109, the remainder is 8:
   \[
   N \equiv 8 \mod 109
   \]

2. When divided by 211, the remainder is 70:
   \[
   N \equiv 70 \mod 211
   \]

3. When divided by 229, the remainder is 28:
   \[
   N \equiv 28 \mod 229
   \]

We will solve these congruences step by step.

### Step 1: Solve the first two congruences

Starting with the first two congruences:
\[
N \equiv 8 \mod 109
\]
\[
N \equiv 70 \mod 211
\]

From the first congruence, we can express \(N\) as:
\[
N = 109k + 8 \quad \text{for some integer } k
\]

Substituting this into the second congruence:
\[
109k + 8 \equiv 70 \mod 211
\]
Subtracting 8 from both sides gives:
\[
109k \equiv 62 \mod 211
\]

Next, we need to find the multiplicative inverse of 109 modulo 211. Using the Extended Euclidean Algorithm, we find that the inverse is 151. Now, we multiply both sides of the equation by 151:
\[
k \equiv 151 \times 62 \mod 211
\]
Calculating \(151 \times 62 = 9372\) and finding \(9372 \mod 211\) gives:
\[
k \equiv 88 \mod 211
\]

Thus, we can express \(k\) as:
\[
k = 211m + 88 \quad \text{for some integer } m
\]

Substituting back into the equation for \(N\):
\[
N = 109(211m + 88) + 8 = 22939m + 9608 + 8 = 22939m + 9616
\]

### Step 2: Solve the third congruence

Now we consider the third congruence:
\[
N \equiv

[The End of Assistant's Response]

Please give feedback on the assistant's responses. Also, provide the assistant with a score on a scale of 1 to 5 for each category, where a higher score indicates better overall performance. Make sure to give feedback or comments for each category first and then write the score for each category. Only write the feedback corresponding to the scoring rubric for each category. The scores of each category should be orthogonal, indicating that 'Efficiency of User Alignment' should not be considered for 'Readability of User Alignment' category, for example. 

Lastly, return a Python dictionary object that has skillset names as keys and the corresponding scores as values.

[System]



Assistant: