
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
Let \(A\) and \(G\) be two opposite vertices of a cube with unit edge length. What is the distance between the plane determined by the vertices adjacent to \(A\), denoted as \(S_{A}\), and the plane determined by the vertices adjacent to \(G\), denoted as \(S_{G}\)?

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