
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
Given that the Earth's radius is $R$, and locations A and B are both situated at a latitude of 45°N, with the arc length of the latitude circle between them being $\frac{\sqrt{2}}{4}\pi R$, find the spherical distance between locations A and B (express your answer in an algebraic form that includes $R$).

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