
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 a regular quadrilateral prism $ABCDA'A'B'C'D'$ with vertices on the same sphere, $AB = 1$ and $AA' = \sqrt{2}$, calculate the spherical distance between points $A$ and $C$.

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