
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 function $f(x)=ax^{3}+b\log _{2}(x+ \sqrt {x^{2}+1})+2$, where $(a,b)$ are constants, if the function has a minimum value of $-5$ on $(-\infty,0)$, determine the behavior of the function $f(x)$ on $(0,+\infty)$.

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