
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
Given a quadrilateral with consecutive sides of lengths 70, 90, 130, and 110 that is inscribed in a circle and also has a circle inscribed in it, and the point of tangency of the inscribed circle to the side of length 130 divides that side into segments of lengths x and y, find the absolute difference between x and y.

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