
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
For which  $n\ge 2$  is it possible to find  $n$  pairwise non-similar triangles  $A_1, A_2,\ldots , A_n$  such that each of them can be divided into  $n$  pairwise non-similar triangles, each of them similar to one of  $A_1,A_2 ,\ldots ,A_n$ ?

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