
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 regular octagon, diagonals have three possible lengths: those that connect adjacent vertices, those that connect vertices two spaces apart, and those that connect vertices three spaces apart. What is the ratio of the shortest diagonal length to the longest diagonal length?

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