
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
Given that the quadratic equation $a x^{2}+b x+c=0$ has no real roots. Person A, due to an error in reading the coefficient of the $x^2$ term, incorrectly found the roots to be 2 and 4. Person B, due to an error in reading the sign of a certain coefficient, incorrectly found the roots to be -1 and 4. What is the value of $\frac{2 b+3 c}{a}$?

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