
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
(1) Find the equation of a line that passes through the intersection point of the two lines $2x+y-8=0$ and $x-2y+1=0$, and is perpendicular to the line $6x-8y+3=0$.
(2) Find the equation of a circle that passes through points $A(5,2)$ and $B(3,-2)$, and has its center on the line $2x-y=3$.

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