
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 \\((x-1)^{2}+y^{2}=25\\) and a line \\(ax-y+5=0\\) that intersects the circle at two distinct points \\(A\\) and \\(B\\).

    \\((1)\\) Find the range of the real number \\(a\\).

    \\((2)\\) If the perpendicular bisector of chord \\(AB\\) passes through point \\(P(-2,4)\\), find the value of the real number \\(a\\).

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