
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
Given the function $f(x) = x^2 + ax + b$, if for any $x, y \in \mathbb{R}$, it always holds that $pf(x) + qf(y) \geq f(px + qy)$, where $p, q$ are real numbers satisfying $p + q = 1$, then determine the range of values for $p$.

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