
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
Consider a rectangle $ABCD$ where $A(0,3)$, $B(0,0)$, $C(4,0)$, $D(4,3)$. Let $E$ be the midpoint of $\overline{AB}$ and $G$ be the midpoint of $\overline{CD}$. Suppose that $\overline{AG}$ and $\overline{BE}$ intersect at point $J$, and $\overline{BD}$ and $\overline{AG}$ intersect at point $K$. Find the area of quadrilateral $BEJK$.

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