How does the Flames of Phlegethos racial feat interact with the sorcerer’s Metamagic option Empowered Spell?

If I have both the Flames of Phlegethos feat and the sorcerer’s Metamagic option Empowered Spell, can I re-roll the same die twice?

The description of the second benefit of the Flames of Phlegethos tiefling racial feat says (XGtE, p. 74):

When you roll fire damage for a spell you cast, you can reroll any roll of 1 on the fire damage dice, but you must use the new roll, even if it is another 1.

The description of the sorcerer’s Metamagic option Empowered Spell reads (PHB, p. 102):

When you roll damage for a spell, you can spend 1 sorcery point to reroll a number of the damage dice up to your Charisma modifier (minimum of one). You must use the new rolls.

You can use Empowered Spell even if you have already used a different Metamagic option during the casting of the spell.

Can you re-roll the same die with both features, or only once? That is, if you re-roll a die with one of these abilities, does the other ability let you re-roll it?

The "You must use the new roll" makes it sound like you cannot, but in general abilities can can override how other abilities work. Is the "keeping the new roll" restriction limited to re-rolls from that ability, or does it apply to all re-rolls from any source?

There is another interpretation of "You must use the new roll." There is a feat called Savage Attacker which reads:

Once per turn when you roll damage for a melee weapon attack, you can reroll the weapon’s damage dice and use either total.

If you compare this to the language in the previous two abilities, you see that the "re-roll and must use the new roll" could be viewed as the alternate to "re-roll and use either roll", and therefore imposes no restriction on other features re-rolling the die.