
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 triangular prism $S-ABC$, $SA$ is perpendicular to the plane $ABC$, and $AB = BC = SA = 1$, with $\angle ABC = \frac{\pi}{2}$.
1. Find the sine of the angle between $SC$ and the plane $ABC$.
2. Find the distance from $B$ to the plane $ASC$.
3. Find the measure of the acute dihedral angle between the planes $SBC$ and $SAC$.

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