
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
(1) There are the following four propositions:  
① The converse proposition of "Congruent triangles have equal areas";  
② If $a^{2}+b^{2}=0$, then $a$ and $b$ are both $0$;  
③ The contrapositive proposition of "If $A∩B=B$, then $A⊆B$";  
Among these, the true propositions are __________ (Fill in the correct proposition numbers).

(2) The maximum value of the function $f(x)=x^{3}-3x^{2}+2$ in the interval $[-1,1]$ is __________.

(3) Let the function $f(x)=x^{3}- \dfrac{x^{2}}{2}-2x+5$, if for any $x∈[-1,2]$, $f(x) > a$, then the range of the real number $a$ is __________.

(4) If $f(x)=3x-x^{3}$ has a minimum value in the interval $(a^{2}-12,a)$, then the range of the real number $a$ is __________.

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