
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 grasshopper can jump exactly 50 cm at a time. It wants to visit 8 points marked on the diagram (each side of the grid cell is 10 cm). What is the minimum number of jumps it needs to make? It is allowed to visit other points on the plane, including points that are not grid nodes. The grasshopper can start and finish at any points.

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