
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 right triangle $ABC$, where $\angle B$ is $90^\circ$ and the sides $AB = 12$ and $BC = 16$. Let $D$ and $E$ be the midpoints of $\overline{AB}$ and $\overline{BC}$ respectively. Lines $\overline{AD}$ and $\overline{CE}$ intersect at point $X$. Compute the ratio of the area of quadrilateral $BDXE$ to the area of triangle $AXC$.

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