Can an Alchemist who is Mythic Tier 2 or higher use Amazing Initiative to use an Extract or drink a Mutagen?
For reference:
At 2nd tier, you gain a bonus on initiative checks equal to your mythic tier. In addition, as a free action on your turn, you can expend one use of mythic power to take an additional standard action during that turn. This additional standard action can't be used to cast a spell. You can't gain an extra action in this way more than once per round.
Everything under the Alchemist's Alchemy(Su) ability sounds like it is NOT spellcasting. They mention it several times.
I'm going to say no for a few reasons. The rules several times refer to extracts being "cast". You are mixing the reagents and adding a magic spark to them, with the drinking being the final somatic component.
For reference:
Alchemists are not only masters of creating mundane alchemical substances such as alchemist's fire and smokesticks, but also of fashioning magical potion-like extracts in which they can store spell effects. In effect, an alchemist prepares his spells by mixing ingredients into a number of extracts, and then “casts” his spells by drinking the extract. When an alchemist creates an extract or bomb, he infuses the concoction with a tiny fraction of his own magical power—this enables the creation of powerful effects, but also binds the effects to the creator.
To be fair, it does also say later "Although the alchemist doesn't actually cast spells", it seems a technicality but RAW you could use it as an argument.
RAI however, amazing initiative is worded as it is to prevent spell casters (which an alchemist effectively is) from casting multiple spells per round. Otherwise mid to late game a caster could cast 3 spells in a round (quicken + amazing initiative). As spells get more powerful and mythic versions are thrown in, that would get truly absurdly unbalanced.
An alchemist could easily do this as well with the trickster path ability assured drinker. Add in combine extracts and the alchemist would have the potential to use 6 extracts in one round. I say no.
