
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 number(s) for the following conclusions:

(1) Given the proposition $p$: $\exists x \in R$, $\tan x = 1$; and the proposition $q$: $\forall x \in R$, $x^2 + 1 > 0$, then the proposition "$p \land \lnot q$" is false.

(2) For the lines $l_1$: $ax + 3y - 1 = 0$, and $l_2$: $x + by + 1 = 0$, the necessary and sufficient condition for $l_1 \perp l_2$ is $\frac{a}{b} = -3$.

(3) The converse of the proposition "If $x^2 - 3x + 2 = 0$, then $x = 1$" is "If $x \neq 1$, then $x^2 - 3x + 2 \neq 0$".

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