
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 that $O$ is the origin, $P$ is any point on the line $2x + y - 2 = 0$, and $\vec{a} = (m, n)$ is a non-zero vector. If the dot product of $\vec{OP}$ and $\vec{a}$ is always constant, find the value of $\frac{m}{n}$.

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