
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
On the board, the number 0 is written. Two players take turns appending to the expression on the board: the first player appends a + or - sign, and the second player appends one of the natural numbers from 1 to 1993. The players make 1993 moves each, and the second player uses each of the numbers from 1 to 1993 exactly once. At the end of the game, the second player receives a reward equal to the absolute value of the algebraic sum written on the board. What is the maximum reward the second player can guarantee for themselves?

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