
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
The golden ratio is the most aesthetically pleasing ratio for a rectangle, where the ratio of width to length is $\frac{{\sqrt{5}-1}}{2}$. Such a rectangle is called a golden rectangle. For example, the facade of the Parthenon in ancient Greece is close to a golden rectangle. Xiao Hua wants to design a poster with a layout in the shape of a golden rectangle. If the width of the poster is $({20+2\sqrt{5}})cm$, what should be the length of the poster in $cm$?

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