
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 positive arithmetic geometric sequence $\{a_{n}\}$, if $3a_{1}$, $\frac{1}{2}a_{3}$, $2a_{2}$ form an arithmetic sequence, calculate the value of $\frac{a_{2016}-a_{2017}}{a_{2014}-a_{2015}}$.

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