
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
To traverse a straight path 10 meters long, a flea uses the following strategy: each day, it covers half of the remaining distance. Thus, it covers 5 meters on the first day, 2.5 meters on the second, and so on (the size of the flea can be disregarded).

(a) How many meters will it have covered by the end of the seventh day? And by the tenth day?

(b) From which day will the flea be less than $0.001 \mathrm{~m}$ away from the end of the path?

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