
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
Chelsea is 60 points ahead halfway through a 120-shot archery competition, where each bullseye scores 10 points and other possible scores are 7, 3, 1, and 0. Chelsea consistently scores at least 3 points per shot. Calculate the minimum number of consecutive bullseyes Chelsea needs over her next $n$ shots to secure victory, assuming her competitor can score a maximum in each shot hereafter.

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