
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
Consider a quadratic polynomial \(q(x) = x^2 - (a+b)x + ab\) where \(a\) and \(b\) are real numbers, and \(q(q(x)) = 0\) has exactly three real solutions. Among these polynomials, find the unique polynomial \( \tilde{q}(x) \) such that the sum of the roots of \(q(x) = 0\) is minimal. What is \(\tilde{q}(2)\)?
- **A)** 7
- **B)** 8
- **C)** 9
- **D)** 10

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