
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
Let  $A = \{m : m$  an integer and the roots of  $x^2 + mx + 2020 = 0$  are positive integers  $\}$ and  $B= \{n : n$  an integer and the roots of  $x^2 + 2020x + n = 0$  are negative integers  $\}$ .
Suppose  $a$  is the largest element of  $A$  and  $b$  is the smallest element of  $B$ . Find the sum of digits of  $a + b$ .

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