
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
There are stones numbered from 1 to 10 around the edge of a circular lake, in clockwise order. The frog Frog starts at stone 1 and jumps in a clockwise direction on these 10 stones.

a) If Frog jumps 2 stones at a time, i.e., from stone 1 to stone 3, from stone 3 to stone 5, and so forth, on which stone will he be after 100 jumps?

b) In the first jump, Frog goes to stone 2, in the second jump to stone 4, in the third jump to stone 7, meaning he skips one more stone than in the previous jump each time. On which stone will Frog be after 100 jumps?

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