
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 two fleas located at the endpoints of the segment \([0,1]\). Certain points within the segment are marked. Each flea can jump over the marked points such that its new position is symmetric with respect to the marked point, and it cannot jump outside the segment \([0,1]\). Each flea jumps independently and can either jump or stay in place in one step. What is the minimum number of jumps required to ensure that both fleas can always end up in the same sub-segment formed by the marked points?

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