
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
Consider a rectangle where one side is thrice the length of the other side. Determine the ratio of the greater diagonal of this rectangle (the diagonal that does not belong to an embedded square) to the diagonal of the square formed by the shorter side.

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