
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
A certain school, in order to support the tourism development conference in our city, has organized a choir competition for each class of the seventh grade. It has been decided to select the class with the best choir performance from the seventh grade to participate in this event. The scores of two classes are as follows:

| Class         | Costume (points) | Pitch (points) | Innovation (points) |
|---------------|-------------------|----------------|---------------------|
| 7th Grade (1) | 90                | 77             | 85                  |
| 7th Grade (2) | 74                | 95             | 80                  |

$(1)$ Calculate the average scores of these three items for both classes and determine which class has a better performance based on the average scores.  
$(2)$ If the scores for costume, pitch, and innovation are determined for each class in the ratio of $1:7:2$, compare which class has a better performance through calculation.

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