
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
Determine the real number solutions for the system of equations where $x + 2y = 5$ and $4xy = 9$. If $x$ is in the form $\frac{a \pm b\sqrt{c}}{d}$, where $a$, $b$, $c$, and $d$ are positive integers and the expression is completely simplified, find the value of $a + b + c + d$.

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