
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
Through a point on the hypotenuse of a right triangle, lines are drawn parallel to the legs of the triangle so that the triangle is divided into a rectangle (instead of a square) and two smaller right triangles. The length and the width of the rectangle are in the ratio 3:1. If the area of one of the two small right triangles is $n$ times the area of the rectangle, what is the ratio of the area of the other small right triangle to the area of the rectangle? Express your answer as a common fraction in terms of $n$.

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