
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 slanted parallelepiped has a base in the shape of a rectangle $ABCD$. The side edges are $AA_1, BB_1, CC_1$, and $DD_1$. A sphere with center at point $O$ touches the edges $BC, A_1B_1$, and $DD_1$ at the points $B, A_1$, and $D_1$, respectively. Find $\angle A_1OB$ if $AD = 4$ and the height of the parallelepiped is 1.

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