
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
Three frogs were sitting on a line. First, one of them jumped, then another, and finally the third one. Each frog landed exactly in the middle of the segment between the other two. It turned out that the lengths of two of these three jumps were 60 cm.

a) What could be the length of the remaining jump?

b) What could have been the initial distance between the two farthest frogs?

(A. V. Shapovalov)

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