
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
Determine the incorrect proposition(s) in the following: \_\_\_\_\_\_
(1) In an arithmetic sequence $\{a\_n\}$, if $a\_m+a\_n=a\_p+a\_q$, then $m+n=p+q$ must hold.
(2) In a geometric sequence $\{a\_n\}$, let $s\_n$ be the sum of its first $n$ terms. Then, $s\_n$, $s\_{2n}-s\_n$, $s\_{3n}-s\_{2n}...$ form a geometric sequence.
(3) In triangle $\triangle ABC$, if $a < b$, then $\sin A < \sin B$.
(4) In triangle $\triangle ABC$, if $a\cos A=b\cos B$, then $\triangle ABC$ is an isosceles right triangle.
(5) In a geometric sequence $\{a\_n\}$, if $a\_4=4$ and $a\_{12}=16$, then $a\_8=8$.

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