
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 the cube $ABCDEFGH$ with opposite vertices $A$ and $G,$ $J$ and $I$ are the midpoints of segments $\overline{AD}$ and $\overline{HE},$ respectively. Let $R$ be the ratio of the area of the cross-section $AGJI$ to the area of one of the faces of the cube. Find the value of $R^2$.

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