
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
We intersected the unit cube $ABCDEFGH$ with a plane such that it intersects the edges $AB$ and $AD$ at the internal points $P$ and $Q$, respectively, both at a distance $x$ from $A$, and it intersects the edge $BF$ at the point $R$. What is the distance $BR$ if $\angle QPR = 120^\circ$?

Present the answer in LaTex format: \boxed{Your answer}
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