
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 the curve $C_n: y = nx^2$, where point $P_n(x_n, y_n)(x_n > 0, y_n > 0)$ is a point on the curve $C_n$ $(n = 1, 2, ...)$. The tangent line of curve $C_n$ at point $P_n$ is $l_n$, which intersects with the $y$-axis at point $Q_n$. If the ratio of the distance from the origin $O(0, 0)$ to tangent line $l_n$ and the length of line segment $P_nQ_n$ reaches the maximum value, then the coordinates of point $P_n$ are \_\_\_\_\_\_.

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