
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
Xiao Kang exercises every day by doing several sets of push-ups, 8 per set, and several sets of pull-ups, 5 per set. On the first day, he did a total of 41 reps (combining both exercises), and he increases the number by 1 each day until the 100th day. If the number of sets of push-ups and pull-ups he does each day are both positive integers, then over these 100 days, Xiao Kang did at least $\boxed{100}$ sets of push-ups and at least $\boxed{106}$ sets of pull-ups.

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