Analyze?
Analyze is a skill used to break down equipment into its more basic components, although this skill often seems useless and random at first I believe that Analyze is a powerful skill if put to the correct use. I have taken it upon myself to uncover the many hidden secrets of this uncharted skill in the hopes that its mystery will bare fruit.
In this Guide you will find first hand accounts and experiences with the skill and a variety of results and explanations.
Enjoy!

The Basics
To avoid clutter, for the basics speak to my sexy cat-girl friend Assistant Blue. She will do her best to explain everything to you about how exactly the process works.
You can find Assistant Blue in Deep Blue, Icicle City (1339/560)

Notes on Function
Assistant Blue will explain that if the number on the Left is lower then the number on the right your Analyze has been successful, although my experience shows me that regardless of timing, success or failure the final product will always result the same. You will receive 1 XP on your Particle Crystal and obtain X number of items in place of the Equipment or Weapon you Analyzed.
A Warning: The Glitch!
All players should be warned before purchasing Wood Catalysts. These items do not work.
Although they can be placed into the slot - when Analyze is used their presence will not register.

Mechanics, Result & Observation
When using Analyze the level of your tool is relative to the number of items you will receive when using the skill.
The level of your fairy and Analyze Skill do not effect the result of your success or failure (Although it is stated they do, or at least should)

A level 1 Particle Crystal will result in a Quantity 3 Analyze.
A level 3 Particle Crystal will result in a Quantity 4 Analyze.
A level 4 Particle Crystal will result in a Quantity ? Analyze. (Undiscovered Currently)
A level 5 Particle Crystal will result in a Quantity ? Analyze. (Undiscovered Currently)
A level 6 Particle Crystal will result in a Quantity ? Analyze. (Undiscovered Currently)
A level 7 Particle Crystal will result in a Quantity ? Analyze. (Undiscovered Currently)

When Analyzing the resulting items are relative to the level of the Equipment consumed and what Catalyst is used when the process is enacted.

CATALYST RESULTS

The bold values are the sell value of the item. I love you all but I wont be giving you short descriptions of each item.

LEVEL 10 EQUIPMENT
Bone
POINTED GOAT HORN 18
TRUMPET SHELL 6
RIDGED SCORPION CARAPACE 9
SMALL CONCH FRAGMENT 10
ANIMAL HORN 50
BAT FANGS 19
RIDGED CRAB CARAPACE 13
GREAT CONCH FRAGMENT 14
BROKEN ANTLER 6
ANIMAL SHARP HORN 11
RAZOR SHARP BEAK 10
CHILLING SNAIL SHELL
SCORPION CARAPACE 3
BLACK SCALE 10
CRAB CARAPACE 12
POISONED THORN 17
HARD SHELL 18
FLOWERY CONCH 10
GIGANTIC ANTLER 11
WOLF FANG 9
GRASS TORTOISE SHELL 6

Water
CONCENTRATED SQUID INK 12
OCTOPUS INK 18
TORTOISE BLOOD 13
CONTAMINATED WATER 9
MURKY WATER 9
BITTER FRUIT 18
TEAR 31
FROZEN SQUID INK 2
HEALING WATER 15
GRASS JUICE 9

Special
BAT WING
STRANGE MASK
RAINBOW GLASS
WHITE SQUIDY CAP
WHITE SQUIRT BANDANNA
CROWN
BEE WING
HEART OF NAIAD
BLACK WINGS
BOTTLE
STRONG GAS
ANCIENT SCROLL FRAGMENT
GLASS
LITTLE SNOW BALL
SQUIRT HANDKERCHIEF

Stone
PINK PEARL 2'500
RED STONE 75
IRON ORE FRAGMENT 50
FLAW SAPPHIRE
PURE IRON ORE 25
NAIAD STONE
BURNING COALS
CLARION SAND
LONG LIZARD TONGUE
IRON ROD 250
COAL ORE
STEEL 125

Food
RAZOR SHARP PINCERS
FROZEN SNAIL FEELERS 22
HYPNOTIC SPORE 14
STRONG PENGUIN FEET 18
FERMENTED HONEY 14
POISONED FRUIT 21
INSECT HIND LEGS 21
SNAIL FEELER 23
SCORPION TAIL 2
CRAB PINCER 15
FAT SQUID TENTACLE 3
ROYAL JELLY 91
SCORPION STINGER 6
OCTOPUS TENTACLE 17
PIG TAIL 7
PENGUIN FEET 18
WEBBED PENGUIN FEET 12
STRONG SQUID TENTACLE 13
BEE ANTENNA 8
FRESH WELK MEAT 9

Again I need mention WOOD Catalysts DO NOT WORK