
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 such that the triangle is divided into a rectangle and two smaller right triangles. The area of one of the two smaller right triangles is $n$ times the area of the rectangle. If the rectangle has length twice its width, 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}
user