
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
Consider the following four propositions:
1. In the planes $α$ and $β$, $α∩β=l$, $a⊂α$, $b⊂β$. If $a$ and $b$ are skew lines, then at least one of them intersects with $l$.
2. If $a, b ∈ R$ and $a + b = 3$, then the minimum value of $2^{a} + 2^{b}$ is $4\sqrt{2}$.
3. For $x ∈ R$, "$z = (1 - x^{2}) + (1 + x)i$ is a purely imaginary number" is a necessary but not sufficient condition for "$lg|x| = 0$".
4. In the sequence of positive terms ${a_n}$, the sum of the first $n$ terms is $S_n$. If $S_n = \frac{1}{2}(a_n + \frac{1}{a_n})$, then $a_n = \sqrt{n} - \sqrt{n-1}, (n∈N_{+})$.

Determine the true propositions by filling in the sequence numbers of the true propositions.

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