
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
Triangular prism \( OAB - O A_{1} B_{1} \) has a plane \( OBB_{1}O_{1} \) that is perpendicular to \( OAB \). Given \(\angle O_{1}OB = 60^{\circ} \), \(\angle AOB = 90^{\circ}\), \(OB = OO_{1} = 2\), and \(OA = \sqrt{3}\), find:
1. The dihedral angle \( O_{1} - AB - O \),
2. The distance \( d \) between skew lines \( A_{1}B \) and \( OA \).

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