
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, the diagonals also have varying lengths. Calculate the ratio of the length of the diagonal spanning one side to the length of the diagonal spanning three sides and express your answer in simplest radical form.

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