
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
Find the average rate of change of the function $y=f(x)=3x^{2}+2$ over the interval $[x_{0},x_{0}+∆x]$, and determine the value of the average rate of change when $x_{0}=2$, $∆x=0.1$.

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