
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
Find all positive integers  $n$  with the  folowing property: for all triples ( $a$ , $b$ , $c$ ) of positive real there is a triple of non negative integers ( $l$ , $j$ , $k$ ) such that  $an^k$ ,  $bn^j$  and  $cn^l$  are sides of a non degenate triangle

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