
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 quadrilateral $ABCD$, sides $AB = 4$, $BC = 3.5$, and $CD = 2$. Assume $\triangle ABC$ and $\triangle BCD$ share a common angle at B where $\angle ABC = \angle BCD = 90^\circ$. Calculate the lengths $AD$ that place the point $D$ such that the areas of $\triangle ABC$ and $\triangle BCD$ become equal.
A) 7.2  
B) 6.3  
C) 6.8  
D) 5.7

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