
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
Determine the number of distinct points in the $xy$-plane common to the graphs of $(x+2y-4)(3x-y+6)=0$ and $(x-y+3)(4x+3y-15)=0$.
A) 0
B) 1
C) 2
D) 3
E) 4
F) $\infty$

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