
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
The function $f(x)=ax^{2}-2020x+2021 (a>0)$, the maximum value of the function $f(x)$ on the interval $\left[t-1,t+1\right] (t\in R)$ is $M$, and the minimum value is $N$. When $t$ takes any real number, the minimum value of $M-N$ is $2$. Find the value of $a$.

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