
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 number 0 is written on the board. Two players take turns to append to the expression on the board: the first player appends either a + or - sign, and the second player appends one of the natural numbers from 1 to 1993. Each player makes 1993 moves, with the second player using each of the numbers from 1 to 1993 exactly once. At the end of the game, the second player’s score is the absolute value of the algebraic sum written on the board. What is the maximum score the second player can guarantee for himself?

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