
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
In cube ABCD-EFGH, points J and I are the midpoints of edges FB and HD respectively. Let R be the ratio of the area of the cross-section EJCI to the area of one face of the cube. Calculate the value of R^2.

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