Word for the point where we stare when in a deep thought [closed]

The word void would work quite nicely.

To a sanctum, past the reaches

Of my fancy and my whim

I sit, glaring at the void

My haggard face grim

I suppose "into the void" would work even better. Not sure why.

Then there is the even "heavier" word abyss. [Sorry, @shaunxer, I came up with this one before you posted your answer! Great minds think alike, I guess!]

To a sanctum, past the reaches

Of my fancy and my whim

I sit, glaring into the abyss

My haggard face grim

Abyss is consonant with sanctum, glaring, haggard, and grim.

Finally, subconscious might work.

To a sanctum, past the reaches

Of my fancy and my whim

I sit, glaring into the subconscious

My haggard face grim

My mum used to refer to that as "staring deep into la-la land" which always amused me. I've often also heard of people "staring off into space" to describe that phenomenon.

Nothingness may fit. Unfortunately, it doesn't rhyme with "reaches".

To a sanctum, past the reaches

Of my fancy and my whim

I sit, staring at nothingness

My haggard face grim

I have seen the phrase "into the middle distance" used in relatively recent novels. Collinsdictionary.com defines this usage of "middle distance" as "halfway between the observer and the horizon". It would seem that this literary usage is derived from a technical term in landscape painting. The Collins page gives this example sentence:

Steam from her coffee cup drifted like mist before her face, and she appeared to gaze into the middle distance, her thoughts hidden.

-from Better than This, Stuart Harrison

I think abyss would be good here, as it is sometimes used when saying something like "staring off into the abyss" like when you are daydreaming.

Also there is a famous quote by Frederich Nietzsche that says

"Battle not with monsters lest ye become a monster; and if you gaze into the abyss the abyss gazes into you

So to complete your sentence you could say

I sit, glaring into the abyss