
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
It is known that in the Cartesian coordinate system, three points A, B, and C lie on a straight line, with $$\overrightarrow{OA} = (-2, m)$$, $$\overrightarrow{OB} = (n, 1)$$, $$\overrightarrow{OC} = (5, -1)$$, and $$\overrightarrow{OA} \perp \overrightarrow{OB}$$, where O is the origin.  
(1) Find the values of the real numbers m and n;  
(2) Let G be the centroid of triangle OAC. If there exists a real number λ such that $$\overrightarrow{OB} = \lambda \overrightarrow{OG}$$, try to find the magnitude of ∠AOC.

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