
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
In a competition, there were 50 shooters. The first shooter scored 60 points; the second - 80; the third - the arithmetic mean of the points of the first two; the fourth - the arithmetic mean of the points of the first three. Each subsequent shooter scored the arithmetic mean of the points of all the previous ones. How many points did the 42nd shooter score? And the 50th?

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