
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 a circle \\(C\\) with its center in the second quadrant, which passes through the intersection point of two lines \\(3x+y-5=0\\) and \\(2x-3y+4=0\\), and is tangent to the line \\(3x-4y+5=0\\) and the \\(x\\)-axis, find the equation of circle \\(C\\).

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