
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}\\), let the function be \\(f(x) = ax - \ln x\\). The tangent line to the graph of \\(f(x)\\) at the point \\((1, f(1))\\) is denoted as \\(l\\). Find the y-intercept of \\(l\\).

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