
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
Triangle $ABC$ has vertices $A(-1,6)$, $B(1,2)$, $C(7,2)$. A vertical line intersects $\overline{AC}$ at $R$ and $\overline{BC}$ at $S$, such that the area of $\triangle RSC$ is 8. Determine the positive difference of the $x$ and $y$ coordinates of point $R$.

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