
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
a) A worm always moves in a straight line. Every day, it goes 5 meters forward and 3 meters backward. At the end of 15 days, how far will the worm be from the starting point?

b) At the end of these 15 days, how many meters in total will the worm have walked?

c) Another worm also moves in a straight line but differently from the first one. On the first day, it moves 1 meter forward and 1/2 meter backward. On the second day, it moves 1/2 meter forward and 1/3 meter backward. On the third day, it moves 1/3 meter forward and 1/4 meter backward, and so on. How many meters will it have walked after 1000 days?

d) Will this second worm ever be 2 meters away from the starting point on any day?

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