
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 $f(x) = ax^2 - (2a+1)x + a + 1$.

1. If $a=2$, solve the inequality $f(x) \geq 0$ for $x$.
2. If for all $a \in [-2, 2]$, it holds that $f(x) < 0$, find the range of values for the real number $x$.

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