
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 $f(x)=\ln(x+m)-x$ ($m$ is a constant) has an extreme value at $x=0$.

(Ⅰ) Find the value of the real number $m$;  
(Ⅱ) Find the maximum value of the function $g(x)=f(x)-x^{2}$ when $x\in\left[-\frac{1}{2},+\infty\right)$.

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