
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]


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Through the midpoints \( M \) and \( N \) of the edges \( A A_1 \) and \( C_1 D_1 \) of the parallelepiped \( A B C D A_1 B_1 C_1 D_1 \), a plane is drawn parallel to the diagonal \( BD \) of the base. Construct the section of the parallelepiped by this plane. In what ratio does it divide the diagonal \( A_1 C \)?

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