
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
Assume plane $\alpha$ is parallel to plane $\beta$. Points $A$, $C$ on plane $\alpha$, and points $B$, $D$ on plane $\beta$. The line $AB$ intersects line $CD$ at point $S$, which is located between plane $\alpha$ and $\beta$. Given that $AS = 8$, $BS = 6$, $CS = 12$, then the length of $SD$ is ______.

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