
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, find the positive difference in the \( x \)-coordinates when lines \( p \) and \( q \) reach \( y = 20 \). Line \( p \) passes through points \( (0, 10) \) 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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