
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 base of a pyramid is a rhombus $ABCD$, and its vertex $E$ is perpendicular to the intersection point $O$ of the diagonals. Furthermore,

$$
OA: OB = OB: OE = 1: \frac{1+\sqrt{5}}{2}.
$$

Calculate the angles between each pair of adjacent faces of the pyramid!

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