
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
For how many positive integral values of $b$ is it true that $x = 3$ is the only positive integer solution of the system of inequalities $$
\begin{cases}
3x > 4x - 4 \\
4x - b > -8
\end{cases}
$$

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