
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
Let \\(f(x)=\ln x-a(x-1)\\) where \\(a \in \mathbb{R}\\).

\\((1)\\) Discuss the monotonicity of the function \\(f(x)\\).

\\((2)\\) If for \\(x \geqslant 1\\), \\(f(x) \leqslant \frac{\ln x}{x+1}\\) always holds, find the range of the real number \\(a\\).

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