
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
A plane passes through the side of the base of a regular quadrilateral pyramid and bisects the dihedral angle at this side. Find the area of the base of the pyramid with the smallest volume, given that the mentioned plane intersects the height of the pyramid at a point that is at a distance \( d \) from the plane of the base.

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