
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 that $f(x) \geq kx + b \geq g(x)$, the line $y = kx + b$ is defined as the "boundary line" for the curves $f(x)$ and $g(x)$. If $$f(x) = x \ln x$$ and $$g(x) = \frac{1}{2} \left( x - \frac{1}{x} \right), x \in [1, +\infty)$$, find the "boundary line" for $f(x)$ and $g(x)$.

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