
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
Given an archery contest with 120 shots, Chelsea is ahead by 70 points after 60 shots, with scoring as 10, 8, 5, 3, or 0 points, and Chelsea scoring at least 5 points per shot. Chelsea will achieve victory by scoring the next n shots as bullseyes (10 points) regardless of her opponent’s scores in the remaining shots. Find the smallest n needed to guarantee her win.

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