
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
Through the midpoint of the edge \( AB \) of a cube \( ABCD A_1 B_1 C_1 D_1 \) with a side length of \( a \), a plane is passed parallel to the lines \( B D_1 \) and \( A_1 C_1 \).

1) In what ratio does this plane divide the diagonal \( D B_1 \)?
2) Find the area of the resulting cross-section.

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