
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  $\Delta$  denote the set of all triangles in a plane. Consider the function  $f: \Delta\to(0,\infty)$  defined by  $f(ABC) = \min \left( \dfrac ba, \dfrac cb \right)$ , for any triangle  $ABC$  with  $BC=a\leq CA=b\leq AB = c$ . Find the set of values of  $f$ .

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