
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 $y = 4$ intersects the graph of $y = 5x^2 + 3x - 2$ at the points $C$ and $D$. Find the distance between $C$ and $D$, expressed in the form $\frac{\sqrt{p}}{q}$, 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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