
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
Let \( q(x) \) be defined on \( 3 \le x \le 15 \) such that
$$
q(x) = \begin{cases} 
x + 2 &\quad \lfloor x \rfloor \text{ is prime} \\
q(z) + (x + 2 - \lfloor x \rfloor) &\quad \text{otherwise}
\end{cases}
$$
where \( z \) is the greatest prime factor of \( \lfloor x \rfloor \). Express the range of \( q \) in interval notation.

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