
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 \\(a \in \mathbb{R}\\), \\(f(x) = a\ln(x - 1) + x\\), \\(f'(2) = 2\\)  
\\((1)\\) Find the value of \\(a\\), and the equation of the tangent line \\(y = g(x)\\) to the curve \\(y = f(x)\\) at the point \\((2, f(2))\\);  
\\((2)\\) Let \\(h(x) = mf'(x) + g(x) + 1\\). If for any \\(x \in [2, 4]\\), \\(h(x) > 0\\), find the range of the real number \\(m\\).

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