
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:
$(1)$ Given the sets $A=\{1,a\}$ and $B=\{1,2,3\}$, the proposition "$a=3$" is a sufficient but not necessary condition for "$A \subseteq B$";
$(2)$ "$x < 0$" is a necessary but not sufficient condition for "$ln(x+1) < 0$";
$(3)$ "The minimum positive period of the function $f(x)=\cos^{2}ax-\sin^{2}ax$ is $\pi$" is a necessary and sufficient condition for "$a=1$";
$(4)$ A necessary and sufficient condition for "the angle between the plane vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ is obtuse" is "$\overrightarrow{a} \cdot \overrightarrow{b} < 0$".
Determine the sequence number(s) of the correct proposition(s). Fill in the blanks with the sequence number(s) of all correct propositions.

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