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When performing high jump and long jumps, the wording of the actions states that you perform a stride of at least 10 feet, then make either a vertical or horizontal Leap. Make an athletics check.
So, if you have a feat that modifies your Leap action, does that affect high or long jumps, since they have a Leap action nested inside of them?
So a feat like Raging Athlete:
"Physical obstacles can’t hold back your fury. While you are raging, you gain a climb Speed and swim Speed equal to your land Speed, the DC of High Jumps and Long Jumps decreases by 10, and your Leap distance increases by 5 feet when you jump horizontally and by 2 feet when you jump vertically."
Obviously it reduces the DC for high and long jumps. But does the last bit about Leap distances also apply to high and long jumps, since the high and long jumps still use the Leap action?
Secondly, how high can you jump with Sudden Leap? Specifically this line:
"When attempting a High Jump or Long Jump during a Sudden Leap, determine the DC using the Long Jump DCs, and increase your maximum distance to double your Speed."
The answer is very clearly yes to me, for the exact reason you stated.
Long Jump and High Jump both contain a Leap Action, with a maximum distance/height, and Feats like Powerful Jump and Raging Athlete raise that maximum.
But others vociferously disagree.