
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
Given the following propositions:

1. In $\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. If $a > b$, then $\cos A < \cos B$, $\cos 2A < \cos 2B$;
2. $a$, $b \in R$, if $a > b$, then $a^{3} > b^{3}$;
3. If $a < b$, then $\frac {b}{a} < \frac {b+x}{a+x}$;
4. Let the arithmetic sequence $\{a_{n}\}$ have a sum of the first $n$ terms as $S_{n}$. If $S_{2016}-S_{1}=1$, then $S_{2017} > 1$.

The sequence numbers of the correct propositions are _______.

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