
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 set
$$
M=\{1,2, \cdots, 2020\},
$$
for any non-empty subset $A$ of $M$, let $\lambda_{A}$ be the sum of the maximum and minimum numbers in the subset $A$. What is the arithmetic mean of all such $\lambda_{A}$?

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