
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
From the diagram below, find the positive difference in the \(x\)-coordinates when lines \(p\) and \(q\) reach \(y = 20.\) Assume line \(p\) passes through points \((0,8)\) and \((4,0)\), and line \(q\) passes through points \((0,5)\) and \((10,0)\).

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