
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: (x-3)^{2} + (y-4)^{2} = 4\\) and a point inside the circle \\(P(2,5)\\).

\\((\\)I\\()\\) Find the equation of the line passing through point \\(P\\) that has the shortest chord length.

\\((\\)II\\()\\) Find the equation of the tangent line passing through point \\(M(5,0)\\) to circle \\(C\\).

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