
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  $F(n)$  denote the smallest positive integer greater than  $n$  whose sum of digits is equal to the sum of the digits of  $n$ . For example,  $F(2019) = 2028$ . Compute  $F(1) + F(2) + \dots + F(1000).$ *Proposed by Sean Li*

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