
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
Tanya took a list of one hundred numbers $1, 2, 3, \ldots, 100$ and crossed out some of them. It turned out that for any two numbers $a$ and $b$ from the remaining numbers, the equation $x^2 + ax + b = 0$ has at least one real root. What is the maximum number of numbers that could remain uncrossed?

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