
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
A circle centered at point \( p \) is tangent to the circle given by the equation \((x+1)^{2} + y^{2} = 1\) externally and is tangent to the circle given by the equation \(x^{2} + y^{2} - 2x - 8 = 0\) internally. Determine the coordinates of the point \( p \) that is the farthest distance from the origin.

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