
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 \( P(0, a) \) be any point other than the origin on the \( y \)-axis. A line passing through the point \( P \) and parallel to the \( x \)-axis intersects the curve \( y = \frac{1}{a} \ln x \) at point \( Q \). The tangent to the curve \( y = \frac{1}{a} \ln x \) at point \( Q \) intersects the \( y \)-axis at point \( R \). Find the minimum value of the area of \( \triangle PQR \).

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