
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
A square is divided into rectangles. It turns out that the areas of all six resulting rectangles are equal. Determine by how many times the longer side of the shaded rectangle is greater than its shorter side. Justify your answer.

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