
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
In a parallelogram  $ABCD$  with the side ratio  $AB : BC = 2 : \sqrt 3$  the normal through  $D$  to  $AC$  and the normal through  $C$  to  $AB$  intersects in the point  $E$  on the line  $AB$ . What is the relationship between the lengths of the diagonals  $AC$  and  $BD$ ?

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