
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
On a large sheet of paper, two very small fleas are jumping. The first jump of the fleas is made towards each other in a straight line (their jumps may have different lengths). The first flea initially jumps to the right, then up, then to the left, then down, then again to the right, and so on. Each of its jumps increases by 1 cm compared to the previous jump. The second flea initially jumps to the left, then up, then to the right, then down, then again to the left, and so on. Similarly, each of its jumps also increases by 1 cm compared to the previous jump. After 100 jumps, the fleas are 3 meters apart. What was the initial distance between the fleas?

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