
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
Let $i$ and $j$ be the unit vectors on the x-axis and y-axis of the Cartesian coordinate system, respectively. If there are three points A, B, and C on the same line, and $\overrightarrow{OA} = -2i + mj$, $\overrightarrow{OB} = ni + j$, $\overrightarrow{OC} = 5i - j$, $\overrightarrow{OA} \perp \overrightarrow{OB}$, find the values of the real numbers $m$ and $n$.

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