
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
Squares $ABCD$, $EFGH$, and $GHIJ$ are identical in area. Point $C$ divides side $IH$ of square $GHIJ$ in the ratio 1:3, starting from $I$ towards $H$, and point $D$ divides side $HE$ in the same ratio, starting from $H$ towards $E$. Determine the ratio of the area of the shaded pentagon $AJICB$ to the sum of the areas of the three squares.

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