epoxidation: substitution vs. conjugation

Bit of a dilemma: trying to figure out which alkene m-CPBA / H₂O₂ in base will react with. I've attached a picture of the starting molecule; there's an internal, more substituted alkene in the ring and there's a terminal one outside of the ring.
I would've thought that since the internal alkene is conjugated with an electron-withdrawing group (the carbonyl group) that that would make the alkene more electron-poor, so the hydroperoxide anion would attack there in a nucleophilic fashion, but the problem is that this alkene is more substituted than the terminal one, which causes the alkene to become more nucleophilic: apparently the electrophilic oxygen on m-CPBA would be attacked by the internal one instead and then H₂O₂ would attack the terminal alkene.

Does this mean that the conjugation has less effect than the fact that it is more substituted? If so, does it mean that the H₂O₂ mechanism is concerted like the m-CPBA one? Bit of a long shot but if anyone replies, thanks

The epoxidation of an electron deficient double bond by hydrogen peroxide is called the Juliá-Colonna epoxidation (https://www.wikiwand.com/en/Juli%C3%A1%E2%80%93Colonna_epoxidation). It is not concerted like epoxidation via MCPBA, it's more akin to an E1_cb.

I would be very cautious using MCPBA in a molecule with a carbonyl, as it's fairly likely Baeyer Villiger oxidation would occur (hydrogen peroxide can also cause this but you would need different reaction conditions).

Thank you for the link, didn't think the H₂O₂ mechanism was concerted. So am I right in thinking that the hydroperoxide anion would attack the alkene that's conjugated with the carbonyl group, even though it's more substituted than the terminal one?

I would think so, yes.