
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, 50 shooters participated. The first shooter scored 60 points; the second scored 80 points; the third scored the arithmetic mean of the points scored by the first two; the fourth scored the arithmetic mean of the points scored by the first three. Each subsequent shooter scored the arithmetic mean of the points of all the previous shooters. How many points did the 42nd shooter score? And the 50th?

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