
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 how many distinct points in the $xy$-plane are common to the graphs of $(x+y-7)(2x-3y+7)=0$ and $(x-y+3)(3x+2y-18)=0$.
A) 0
B) 1
C) 2
D) 3
E) 4
F) Infini

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