
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 $f(x)=-a\ln x+(a+1)x-\frac{1}{2}x^{2}(a > 0)$.
(1) Discuss the monotonicity of the function $f(x)$;
(2) If $f(x)\geqslant -\frac{1}{2}x^{2}+ax+b$ always holds, find the maximum value of the real number $b$ when $a\in[\frac{1}{2},1]$.

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