
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
There are 68 pairs of non-zero integers on the blackboard. For a positive integer \( k \), at most one pair among \((k, k)\) and \((-k, -k)\) appears on the blackboard. A student erases some numbers from these 136 numbers so that the sum of any two erased numbers is not zero. If at least one number from a pair of the original 68 pairs is erased, the student gets one point. Find the maximum score the student can achieve. Note: The 68 pairs can have some identical pairs.

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