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ACROSS

 1 Right and left (found in office tent) are scrambled, having given it some thought (5,10)

 9 Lustrous blaze I give off (9)

10 Tooth 1A in 29 would be good (5)

11 Officer 1A in 29 would be a forensic professional (7)

12 What God supposedly did 1A in 29 would be like an athlete’s shoe (7)

13 Dances 1A in 29 would be lascivious glances (5)

15 Almost overdue, by way of a European country (6)

19 Pole, for instance, spun around that thing’s innards (6)

20 Baseball requirement 1A in 29 would be wood (5)

23 Backward movement 1A in 29 would be missing limbs (7)

25 Legal proceedings 1A in 29 would be shows (7)

27 Expression of displeasure 1A in 29 would be sent by air (5)

28 “Typify zip!” I emote foolishly (9)

29 Thankless gigolo shattered Carroll’s mirror (3,7,5)

DOWN

 1 Tuna and cobra stewed in beer (8)

 2 Plowman catching home run? That’s exciting (8)

 3 Authority’s downfall is pronounced (5)

 4 Meaningless repetition confused Alice when adopting Spanish greeting (9)

 5 In Honolulu, dickering is playful (5)

 6 On the way to accommodate favorite in contention (9)

 7 Listen: Enlist silent tinsel to provide four ways to supply what you need to make bays (6)

 8 Maneuver under a Nobel-winning poet (6)

14 Easily enter cunning racket (also on the phone) (5,4)

16 Satan: “I’m an eccentric, like many devils” (9)

17 Somalian touched up a painting (4,4)

18 Bits of ears, some used more than once? Think again (8)

21 Gain is anti-inappropriate? (6)

22 Pay no attention to contents of sign or evidence (6)

24 Move mountains bottom to the top, say (5)

26 Carry trail mix up, taking north fork (5)

SOLUTION TO PUZZLE NO. 3364

ACROSS 1 ARCH(R)IVAL 6 hidden 9 letter bank 10 DOCK + ET 11 anag. 12 SEED + O + UBLE (anag.) 14 BEN + D 16 init. letters 18 AUSTER + [p]ITY 21 MISS + POKE 22 NUN C.I.O. 25 AT THE LAST + MINUTE 26 HI + RED 27 DAM + A SCENE

DOWN 1 A(WAR)D 2 CUTI(CL)E 3 anag. 4 anag. 5 anag. 6 LE(ANT)O 7 GR(IMAC)E 8 CANA(DAD)RY 12 S(TEAM + BAT)H 13 B(LACK + H)AND 15 BE(AU + TI)ES 16 VI + SITOR (rev.) 19 “ink, lewd” 20 S + P + READ 23 phonetic hidden 24 A + TOM