
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
The correct proposition number(s) among the following:

1. Given that $m$ and $n$ represent two different lines, $α$ and $β$ represent two different planes, and $m ⊥ α$, $n ⊂ β$, then "$α ⊥ β$" is a necessary but not sufficient condition for "$m // n$".
2. There is no $x ∈ (0, 1)$ that makes the inequality $log_2 x < log_3 x$ hold.
3. The converse of the proposition "if $am^2 < bm^2$, then $a < b$" is a true proposition.
4. For all $θ ∈ R$, the function $f(x) = sin(2x + θ)$ is never an even function.

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