
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
Find the number of common points in the following system of equations:
\[
(x - y + 3)(4x + y - 5) = 0 \text{    and    } (x + y - 3)(3x - 4y + 6) = 0
\]
A) 2
B) 3
C) 4
D) 6
E) Infinite

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