
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
Determine (correct with "√", incorrect with "×")

  (1) The average rate of change $\dfrac{\Delta y}{\Delta x}$ of the function $f(x)=c$ (where $c$ is a constant) over the interval $[x_{1},x_{2}]$ is $0.$    

  (2) The derivative of the function $y=f(x)$ at $x=x_{0}$ is independent of the sign of $\Delta x.$    

  (3) The instantaneous rate of change is a physical quantity that describes how fast the function values change over the interval $[x_{1},x_{2}].$    

  (4) In the definition of the derivative, neither $\Delta x$ nor $\Delta y$ can be zero.

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