
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 right triangular prism $A B O - A_1 B_1 O_1$, $O O_1=4, O A=4, O B=3$, $\angle A O B=90^{\circ}$, $D$ is the midpoint of segment $A_1 B_1$, and $P$ is a point on the lateral edge $B B_1$. If $O P \perp B D$, find the angle between $O P$ and the base $A O B$ (express the result in terms of an inverse trigonometric function).

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