Circular Reasoning

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Each clue can be read as both a straight crossword clue and as the wordplay portion of a cryptic clue.

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The clues can be arranged into cycles, where the straight answer for one clue is the same as the cryptic answer for the next clue in the cycle.

stuck, help, how, to, solve, clues

[I expect any team that asks for a hint on this puzzle will be stuck on solving the clues and not the other steps. In this case, we should confirm which answers they have correct and help them out on some answers they don't have. Maybe start by telling them what kind of cryptic clues each one is (homophone, charade, etc.) and letting them know to contact us if they're still stuck and we can give more direct hints then]

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You will end up with 6 cycles (one of which has size 1 because it consists of a single &lit clue). There is a word in each cycle that provides an ordering.

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Order the cycles by which NATO alphabet letter they contain, and convert the lengths to letters alphanumerically to get your 6-letter answer.

A mom or dad song
A record has some
Amend's strip
Animated film "neighbor"
Back, arm and guts
Beginning from wood, transform artfully
Chickens' sound
Component of white chocolate
Curtain call?
Data type for falsehood
Downside to busy airports
Eats audibly
Endlessly endure inner agony
Even-handed
Evolution of dalet
Fix or heal
Fluid customary unit
Funnily, both a rail and a loon
Guy off alone
Headgear outside around the end of time at a university
In chimpanzees, one becoming others' leader
Large medieval center around Pakistan's eastern border
Low point / a spoken farewell
Meat with backstrap
Noisy apparition
Offers having a ribbon topper
Origin of cosmic luck
Piglet store, maybe
Pirouetting garb
Primary verdicts in one's surgery
Put 2 and 2 together, say
Result of countering basketball official with swears
Sandiego's organization
Sneaky figure backing a wrongful act
Some of the smallest amphibians
Source of reverberations in a cave
Start to card and Parker
Steal a piece of eight from a sailing ship
Step back and jump
Talk at length about oneself
To root (out)
Vehicle intended for transportation back to Kansas
Visible on the surface
Weather phenomena that bring in the start of rainstorms