
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
In a space, five points are marked. It is known that these are the centers of spheres, four of which touch each other externally in pairs and touch the fifth sphere internally. Moreover, it is impossible to determine which point is the center of the encompassing sphere. Find the ratio of the radii of the largest and smallest spheres.

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