
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  $f:S\to\mathbb{R}$  be the function from the set of all right triangles into the set of real numbers, defined by  $f(\Delta ABC)=\frac{h}{r}$ , where  $h$  is the height with respect to the hypotenuse and  $r$  is the inscribed circle's radius. Find the image,  $Im(f)$ , of the function.

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