
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 $f(x)=\ln(ax+1)+ \frac{1-x}{1+x}$, where $x\geqslant 0$ and $a > 0$.

(Ⅰ) If $f(x)$ has an extremum at $x=1$, find the value of $a$;  
(Ⅱ) Determine the intervals of monotonicity for $f(x)$;  
(Ⅲ) If the minimum value of $f(x)$ is $1$, find the range of values for $a$.

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