
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 \( 4x + 3 \), and the denominator is \( 9 - 3x \). If \( x \) can have any value between \( -1 \) and \( 3 \), inclusive, determine the values of \( x \) for which the numerator is greater than the denominator.
**A)** \( -1 \leq x \leq 3 \)  
**B)** \( \frac{6}{7} \leq x \leq 3 \)  
**C)** \( \frac{6}{7} < x \leq 3 \)  
**D)** \( 0 \leq x \leq 3 \)

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