
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 lines $l$ and $m$ on a coordinate grid where:
- Line $l$ passes through $(0,4)$ and $(4,0)$,
- Line $m$ passes through $(0,3)$ and $(6,0)$.
Find the positive difference in the $x$-coordinates when $l$ and $m$ reach $y = 10$.

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