
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 circle passes through the intersection points of any two of the lines \( y = x \), \( y = 2x \), and \( y = 15 - 0.5x \). What is the length of the chord of the circle that lies on the line \( x + y = 16 \)?

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