
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
Identify the correct conclusion(s) from the following list (indicate the serial number):

① The negation of the proposition "For all $x \in \mathbb{R}$, $x^2 + x + 1 > 0$" is: "There exists an $x \in \mathbb{R}$ such that $x^2 + x + 1 < 0$."
② The converse of the proposition "If $ab = 0$, then $a = 0$ or $b = 0$" is "If $ab \neq 0$, then $a \neq 0$ and $b \neq 0$."
③ Given the linear regression equation $\hat y = 3 + 2x$, the exact value of the dependent variable for the independent variable value of $2$ is $7$.
④ If $a, b \in [0, 1]$, then the probability that the inequality $a^2 + b^2 < \frac{1}{4}$ is satisfied is $\frac {\pi }{4}$.

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