
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
Two pairs $(x,y)$ of real numbers satisfy the equations $x + y + xy = 4$ and $3xy = 4$. Find $x$ and express it in the form $x = \frac{a \pm b\sqrt{c}}{d}$ where $a$, $b$, $c$, and $d$ are positive integers and the expression is completely simplified. What is the value of $a + b + c + d$?

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