
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
A point on the hypotenuse of a right triangle divides the triangle into three parts: a square and two smaller right triangles, when lines are drawn parallel to the triangle's legs from the point. The area of one of the smaller right triangles is \(m\) times the area of the square. If the side of the square is assumed to be \(2\) units, find the ratio of the area of the other small right triangle to the area of the square, expressing your answer as a fraction in terms of \(m\).

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