
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 a cube ABCD-A1B1C1D1 with edges of length 5, where points E, F, and G are on edges C1D1, AB, and CD respectively, and D1E=AF=DG=1. If sphere O is the circumcircle of the tetrahedron BEFG, then the area of the circle obtained by cutting sphere O with plane BDD1B1 is ______.

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