
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 linear equation in $x$ and $y$: $(a-3)x + (2a-5)y + 6-a = 0$, for each value of $a$, there is an equation, and these equations have a common solution.  
(1) Find this common solution;  
(2) Please explain why, no matter what value $a$ takes, this common solution is always a solution to the linear equation $(a-3)x + (2a-5)y + 6-a = 0$.

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