
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
\[ f(x) = \ln(ax + 1) + \frac{1 - x}{1 + x} \quad (x \geq 0, a > 0). \]

(1) If \( f(x) \) has an extremum at \( x = 1 \), find the value of \( a \).

(2) If \( f(x) \geq \ln 2 \) is always true, determine the range of values for \( a \).

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