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sAdhakatamaG karaNam

साधकतमं करणम् ONPANINI 14042

What helps most is the /karaNa (instrument).

This can be also translated as

The instrument role means the tool that helps to the success of the action the most.

So the axe and the chariot are instruments in —

parazunA chinatti परशुना छिनत्ति "he cuts it with an axe"

rathena gacchati रथेन गच्छति "he goes by chariot".

An instrument takes third ending by kartRkaraN....

Why do we say "most"?

I am not sure, sorry. Maybe this word is supposed to mean that only one instrument is allowed per root. See candravasu.

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I am not sure. I guess that /pANini means that in sentences like "the chef cooks rice with a pan in the kitchen on the fire", all the roles (chef, rice, pan, fire, kitchen) help to the success of the cooking, but only the pan can be /kAraka because it is a tool specifically made for cooking.