
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
Given that vertex $E$ of right $\triangle{ABE}$, with $\angle AEB = 90^{\circ}$, is located halfway along the diagonal $AC$ of unit square $ABCD$, let $R$ be the region consisting of all points inside $ABCD$ and outside $\triangle{ABE}$ whose distance from $AD$ is between $\frac{1}{4}$ and $\frac{1}{2}$. Calculate the area of the region $R$.

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