
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 $a > 0$.
(1) If $f(x)$ has an extremum at $x=1$, find the value of $a$;
(2) If the minimum value of $f(x)$ is 1, determine the range of values for $a$.

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