
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
A quadrilateral with consecutive side lengths $80, 100, 140, and 120$ is inscribed in a circle and has a circle inscribed within it. The point of tangency of the inscribed circle to the side of length $140$ divides it into segments of length $x$ and $y$. Determine the value of $|x-y|$.

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