
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 class held a math competition with a total of 10 questions, each worth 10 points. $\frac{3}{19}$ of the students got all the questions correct, $\frac{13}{19}$ of the students got an average of 5 questions correct, and the rest of the students got all the questions wrong. What is the average score of the students in this math competition?

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