
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 numbers  $1,\frac12,\frac13,\ldots,\frac1{1999}$  are written on a blackboard. In every step, we choose two of them, say  $a$  and  $b$ , erase them, and write the number  $ab+a+b$  instead. This step is repeated until only one number remains. Can the last remaining number be equal to  $2000$ ?

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