
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 and the y-coordinate difference when the x-coordinate is 5 for lines $p$ and $q$ when both lines reach $y = 10$. Line $p$ passes through points $(0,3)$ and $(4,0)$, and line $q$ passes through points $(0,6)$ and $(6,0)$.

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