
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
It is known that the average score of 5 students in a study group who took an academic level test (full score 100) is 80, among them, two girls scored 85 and 75 respectively, and the variance of the scores of three boys $x_1$, $x_2$, $x_3$ is 150 (in square points).  
(1) What is the average score of the three boys $x_1$, $x_2$, $x_3$?  
(2) Calculate the variance of the scores of all 5 students in the study group.

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