
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
Let the function $f(x)= \frac {1}{2}mx^{2}-2x+\ln (x+1)$ where $m\in\mathbb{R}$.  
(I) Determine whether $x=1$ can be an extremum point of the function $f(x)$, and explain the reason;  
(II) If there exists $m\in[-4,-1)$ such that the function $g(x)=f(x)-\ln (x+1)+x^{3}$ defined on $[1,t]$ attains its maximum value at $x=1$, find the maximum value of the real number $t$.

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