
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
Rectangles $ABCD$, $EFGH$, and $GHIJ$ are placed adjacently forming a larger rectangle. The lengths of $AB$ and $GH$ are 2, and the widths of $BC$ and $HI$ are 1. Points $C$ and $D$ are located 1/3rd of the way along side $IH$ and $HE$, respectively, from point $H$. Calculate the ratio of the area of shaded pentagon $AJICB$ to the sum of the areas of the three rectangles.
**A)** \(\frac{1}{12}\)
**B)** \(\frac{1}{9}\)
**C)** \(\frac{5}{36}\)
**D)** \(\frac{1}{6}\)
**E)** \(\frac{1}{18}\)

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