
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
The line $y = 2$ intersects the graph of $y = 3x^2 + 2x - 5$ at the points $C$ and $D$. The distance between $C$ and $D$ can be written as $\frac{\sqrt{p}}{q}$, where $p$ and $q$ are positive integers that do not share any factors other than one. Find the value of $p - q$.

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