
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 numerator of a fraction is given by $4x + 3$, and the denominator is $8 - 3x$. If $x$ can have any value between $-1$ and $3$, determine the values of $x$ for which the numerator is greater than twice the denominator.
A) $-1 \le x \le \frac{13}{10}$  
B) $\frac{13}{10} < x \le 3$  
C) $-1 < x \le 3$  
D) $3 < x \le 4$  
E) None of these

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