
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
Points \( B_1, C_1, D_1 \), and \( A_1 \) are taken on the extensions of the sides \( AB, BC, CD \), and \( DA \) of a convex quadrilateral \( ABCD \) such that \( BB_1 = AB \), \( CC_1 = BC \), \( DD_1 = CD \), and \( AA_1 = DA \). By how many times is the area of quadrilateral \( ABCD \) smaller than the area of quadrilateral \( A_1B_1C_1D_1 \)?

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