
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
Positive integers $c$ and $d$ are such that the graphs of $y=2cx+10$ and $y=6x+d$ intersect the $x$-axis at the same point. What is the sum of all possible $x$-coordinates of these points of intersection?
A) -30
B) -25
C) -20
D) -17
E) -15

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