Unable to enter Recovery Mode -2006F

I'm using a MacBook Air (11-inch, Mid 2013). I recently reformatted and reinstalled the OS via Internet Recovery, but I suspect something went wrong.

Now, when I boot normally, I get the infamous Flashing Question Mark.

When I boot with Alt+Cmd+R, I get the spinning globe with

Starting Internet Recovery. This may take a while

and then:

apple.com/support
-2006F

When I boot with Cmd+R, I get the exact same thing as above. Maybe my Recovery Partition is corrupted, so it defaults to Internet Recovery?

This MacRumors thread Flashing Question mark in folder after start up seems similar to my problem, but the OP is able to get into Internet Recovery, unlike me.

Any suggestions?

Considering you can't boot into an OS, the first things I'd try are resetting the NVRAM and SMC. Below are the steps for doing so, as well as the order you should do it.

1. Reset the NVRAM

Older Macs had what's called Parameter RAM (PRAM), newer Macs use Non-Volatile Random-Access Memory (NVRAM). Here’s how to reset it on your particular Mac:

1. Shut down your machine. Yes, a full shut down, not just logging out.
2. Press the power button and then press the commandoptionpr keys. You have to make sure you press these keys before the gray screen appears or it won’t work.
3. Hold those keys down until your Mac reboots again and you here the startup chime.
4. Let go of the keys and let your Mac reboot normally.

Note: When you log back in you may need to readjust some of your system preferences (e.g. speaker volume, screen resolution, startup disk selection, time zone information, etc).

2. Reset the SMC

Here’s what you do to reset the SMC on your particular Mac:

1. Shut down your computer
2. Keep the MagSafe adapter (power cable) plugged in.
3. Press at the same time shiftoptioncontrol (on the left side of the keyboard) and the power button
4. Let go
5. Turn your computer back on with the power button.

Once you've done both of these, check to see whether the problem behaviour (i.e. an inability to enter Internet recovery) is still present. Let me know how you go.