
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 that Chelsea leads by 75 points after 100 shots in a 150-shot archery competition, with each score being 10, 8, 5, 1, or 0, and Chelsea scores at least 5 points on each shot, determine the minimum value of n needed for Chelsea to guarantee victory after scoring bullseyes on her next n shots.

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