
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 $\frac{1}{2} \leqslant \frac{a_{n+1}}{a_{n}} \leqslant 2$ for all $n \in \mathbb{N}^{*}$, $a_{1}=1$, $a_{2}=\frac{3}{2}$, and $a_{4}=4$, determine the range of values for $a_{3}$.

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