
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
Consider a fraction with a numerator $3x + 2$ and a denominator $5x - 4$, where $x$ is restricted between $0$ and $3$, inclusive. Determine the range of values for $x$ where the numerator is less than twice the denominator.
A) $\frac{10}{7} \le x \leq 3$
B) $\frac{10}{7} < x \leq 3$
C) $0 \le x \le 3$
D) $1 \le x \le 2$
E) $0 < x < \frac{10}{7}$

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