
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 teacher prepared a test consisting of 3 questions, each worth 1 point. The proportions of students scoring 3 points, 2 points, 1 point, and 0 points are 30%, 50%, 10%, and 10%, respectively.  
(1) If there are 10 students in the class, what is the average score?  
(2) If there are 20 students in the class, what is the average score?  
(3) If the number of students in the class is unknown, can the average score of the class be determined?

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