You are an AI assistant. User will you give you a task. Your goal is to complete the task as faithfully as you can. While performing the task think step-by-step and justify your steps.
system
Given an input stream, the objective of this task is to classify whether words in the stream are grammatically correct or not. The input to this task is a stream of words, possibly from captions generated by a speech-to-text engine, and the output is a classification of each word from the labels (reason) = [NO_DIFF (correct), CASE_DIFF (case error), PUNCUATION_DIFF (punctuation error), CASE_AND_PUNCUATION_DIFF (both case and punctuation error), STEM_BASED_DIFF (stem word error), DIGIT_DIFF (digit error), INTRAWORD_PUNC_DIFF (intra-word punctuation error), and UNKNOWN_TYPE_DIFF (an error that does not corrrespond to the previous categories)].
Q: ['so', "let's", 'say', 'that', "we've", 'got', 'the', 'polynomial', '16', 'X', 'to', 'the', 'third', 'plus', '24', 'x', 'squared', 'plus', '9x', 'now', 'what', "I'd", 'like', 'you', 'to', 'do', 'is', 'pause', 'the', 'video', 'and', 'see', 'if', 'you', 'can', 'factor', 'this', 'polynomial', 'completely', 'now', "let's", 'work', 'through', 'it', 'together', 'so', 'the', 'first', 'thing', 'that', 'you', 'might', 'notice', 'is', 'that', 'all', 'of', 'the', 'terms', 'are', 'divisible', 'by', 'X', 'so', 'we', 'can', 'actually', 'factor', 'out', 'an', 'X', 'so', "let's", 'do', 'that', 'and', 'actually', 'if', 'we', 'look', 'at', 'these', 'coefficients', 'it', 'looks', 'like', "let's", 'see', 'it', 'looks', 'like', 'they', "don't", 'have', 'any', 'common', 'factors', 'other', 'than', 'one']
A:
user
To complete this task, I will go through the input word stream and classify each word based on the given labels. I will do this step-by-step:

1. Initialize a list called 'output' to store the classification results for each word.
2. Go through each word in the input stream.

For each word:
- Check if it has the correct case. If not, it may be a CASE_DIFF error.
- Check if it has the correct punctuation. If not, it may be a PUNCUATION_DIFF error.
- Check if it is a stemmed word. If it is, it may be a STEM_BASED_DIFF error.
- Check if it is a digit. If it is, it may be a DIGIT_DIFF error.
- Check if it has an intra-word punctuation error. If it does, it may be an INTRAWORD_PUNC_DIFF error.
- If none of the above errors apply, it might be an UNKNOWN_TYPE_DIFF error.
- If no errors are found, label it as NO_DIFF (correct).

3. Append the classification label to the 'output' list.

4. Return the 'output' list.

A: ['NO_DIFF', 'INTRAWORD_PUNC_DIFF', 'NO_DIFF', 'NO_DIFF', 'INTRAWORD_PUNC_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'DIGIT_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_D...RAWORD_PUNC_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'INTRAWORD_PUNC_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'NO_DIFF', 'INTRAWORD_PUNC_DIFF', 'NO_DIFF']
assistant