
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
Given the sequence $\{a_{n}\}$ that satisfies $a_{1}=\frac{1}{2}$, $a_{n+1}-a_{n}=p\cdot 3^{n-1}-nq$, where $n\in\mathbb{N}^{*}$, $p$, $q\in\mathbb{R}$. If $p=1$ and $a_{4}$ is the minimum term of the sequence $\{a_{n}\}$, find the range of values for $q$.

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