
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
Consider the quadratic equation $x^2 + (2q-1)x + q = 0$, where $q$ is a positive number. If the roots of this equation differ by 2, find the value of $q$.
A) $2 + \sqrt{6}$
B) $1$
C) $1 + \frac{\sqrt{7}}{2}$
D) $3$

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