
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
On the extensions of the sides \(AB\), \(BC\), \(CD\), and \(DA\) of the convex quadrilateral \(ABCD\), points \(B_1\), \(C_1\), \(D_1\), and \(A_1\) are taken respectively such that \(BB_1 = AB\), \(CC_1 = BC\), \(DD_1 = CD\), and \(AA_1 = DA\). By how many times is the area of quadrilateral \(A_1B_1C_1D_1\) greater than the area of quadrilateral \(ABCD\)? (10 points)

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