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BEGINNER GUIDE:

First time [Saryn]? Here's how to play: press 1(Spores) at the enemy, and...
If you have Toxic Lash (3) active, it's enough to just hit an enemy to spread spores (and while we're here, can I request on behalf of everyone to change energy color of your [Ignis] to something dark?)
If you don't, then killing enemy with anything other than spores themselves will spread them anyway.

Once [Venom Dose] is installed, hold 1 to buff weapons with (strength%) corroside damage, for yourself and allies in range.

Miasma (4) deals 4x damage to enemies affected by spores (or if you're the glass-half-empty kind of person, it only deals 1/4 damage to enemies not affected by spores).
Use against large groups for maximum satisfaction.

PROGRESSION ORDER:
Part 1 - no requirements (no forma, no reactor, no exilus):

Any aura you can fit, just for the capacity.

Venom Dose - can purchased from Red Veil or Steel Meridian, or from other players. It helps your team, and it's especially good for weapons that are not fully modded. I'm still using it for endgame content, so I'm giving it the top priority.

Naramon polarity(-): Stretch and/or Augur Reach - range is cheapest and most important stat, and in the final build both of them will be used.
[Streamline] helps with energy (especially before a certain quest...), but if there are no issues then range is better.

Vazarin polarity(D): [Overextended] or [Adaptation] if available, otherwise [Vitality] is a good placeholder (stop at rank 6 or 8).

[Saryn Prime] has an extra free Madurai polarity(V): [Blind Rage] or [Transient Fortitude] if available, otherwise [Intensify] or [Cunning Drift] (not in exilus slot)

Arcanes are completely optional, I have not experienced any real need for Energize unless spamming 4 for no reason, but it's used in the final build because spamming 4 for no reason is fun for some reason.

Part 2 - if/once you have Saryn Prime: install reactor/forma/exilus as needed.
If you're new: once you're done with The Second Dream, buy and install a built Lua Zenurik Lens from market.
Umbral Vitality/Fiber/[Intensify] are from The [Sacrifice]. They're not mandatory, but not dying is a huge QoL improvement.

Forma priority: Aura > Umbra > Zenurik (=) = Naramon(-)
Exilus: Vazarin(D) for Primed Sure Footed once available (daily login reward on day 400 / 600 / 900) - by the time you get it, you'll most likely understand why you need it.

Rank priority: Umbral Intensify >> Blind Rage/Transient Fortitude > Adaptation > Umbral Fiber = Vitality

How to heal: Magus Repair / Arcane Grace / subsume something like Sevagoth's Gloom (but I don't recommend it).

Helminth/subsume: can't go wrong with [Rhino]'s Roar, it buffs both weapons and abilities, for yourself and allies.

Archon shards: yes.