
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 the equations $(x+2y-6)(2x-y+4)=0$ and $(x-2y+3)(4x+y-10)=0$, find the number of distinct points in the $xy$-plane common to the graphs of these equations.

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