
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 the cube \(A B C D A^{\prime} B^{\prime} C^{\prime} D^{\prime}\) with edge length \(a\), a cross-section is made by a plane parallel to the plane \(B D A^{\prime}\) and at a distance \(b\) from it. Find the area of the cross-section.

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