
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
Define the function \(q(x)\) on the interval \(1 \leq x \leq 15\) such that
$$q(x) = \begin{cases} x + 2 &\quad \text{if } \lfloor x \rfloor \text{ is prime,} \\ q(y) + (x + 2 - \lfloor x \rfloor) &\quad \text{otherwise,} \end{cases}$$
where \(y\) is the greatest prime factor of \(\lfloor x \rfloor\). Determine the range of \(q\) in interval notation.

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