
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) "The sequence $\{a\_n\}$ is a geometric sequence" is a necessary but not sufficient condition for "the sequence $\{a\_n a_{n+1}\}$ is a geometric sequence";
(2) "$a=2$" is a necessary and sufficient condition for "the function $f(x)=|x-a|$ is an increasing function on the interval $[2,+∞)$";
(3) "$m=3$" is a necessary and sufficient condition for "the line $(m+3)x+my-2=0$ is perpendicular to the line $mx-6y+5=0$";
(4) Let $a$, $b$, $c$ be the sides opposite to angles $A$, $B$, $C$ of $\triangle ABC$, respectively. If $a=1, b= \sqrt {3}$, then "$A=30^{\circ}$" is a necessary but not sufficient condition for "$B=60^{\circ}$".
Find the sequence number(s) of the true proposition(s).

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