
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 the cyclic quadrilateral ABCD, the sides AB and CD are parallel, suggesting that ABCD might be a trapezoid, and it's given that AB = 5 and CD = 9. The diagonals of the quadrilateral intersect at point E on AB such that AE = 1 and EB = 4. Additionally, it's given that BC = 6. If we consider the quadrilateral geometrically accurate and relevant relations consistent, determine the length of the line segment from the midpoint of diagonal BD to the midpoint of diagonal AC.
A) 0
B) 1
C) 5
D) 6

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