
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
Let  $A_1,B_1,C_1,D_1$  be the midpoints of the sides of a convex quadrilateral  $ABCD$  and let  $A_2, B_2, C_2, D_2$  be the midpoints of the sides of the quadrilateral  $A_1B_1C_1D_1$ . If  $A_2B_2C_2D_2$  is a rectangle with sides  $4$  and  $6$ , then what is the product of the lengths of the diagonals of  $ABCD$  ?

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