Action modifier question - CrimethInc. and Monkey Wrench

[DeathInABottle]

To use CrimethInc., I must have performed an action that requires an
anarch. If I bled using Monkey Wrench as a modifier, would that bleed
action have "required" an anarch? My suspicion is that it doesn't,
but I'd be happy to hear otherwise.

CrimethInc. [TR:C]
Cardtype: Action Modifier
Discipline: Protean/Quietus/Thaumaturgy
Requires an anarch. Play after resolving a successful action that
requires an anarch or makes this vampire an anarch.
[pro] Untap this anarch.
[qui] Untap another ready anarch.
[tha] Put this card in play. During your minion phase, you may burn a
pool to untap a ready anarch you control.

Monkey Wrench [TR:C]
Cardtype: Action Modifier
Cost: X blood
Requires an anarch.
+X bleed. X must be 1, 2 or 3. You cannot play another action modifier
to increase this bleed amount.

[LSJ]

DeathInABottle wrote:
> To use CrimethInc., I must have performed an action that requires an
> anarch. If I bled using Monkey Wrench as a modifier, would that bleed
> action have "required" an anarch? My suspicion is that it doesn't,

Correct. Most any minion can take that cardless bleed action.