
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
Determine the correct conclusion(s) among the following:

1. If proposition $p$: $\exists x \in \mathbb{R}$, $\tan x = 1$; proposition $q$: $\forall x \in \mathbb{R}$, $x^2 - x + 1 > 0$. Then the proposition "$p \wedge \neg q$" is a false proposition.
2. Given lines $l_1$: $ax + 3y - 1 = 0$, $l_2$: $x + by + 1 = 0$. The necessary and sufficient condition for $l_1 \perp l_2$ is $\frac{a}{b} = -3$.
3. The contrapositive of the proposition "If $x^2 - 3x + 2 = 0$, then $x = 1$" is "If $x \neq 1$, then $x^2 - 3x + 2 \neq 0$".

The correct conclusion number(s) is/are \_\_\_\_\_\_.

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