
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

The height $A A_1$ of a rectangular parallelepiped $A B C D A_1 B_1 C_1 D_1$ is twice the length of each side of its base. Find the angle between the lines $B D_1$ and $A M$, where $M$ is the point of intersection of the diagonals of the face $D C C_1 D_1$.

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