
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 functions $f(x) = -x^2 - 3$ and $g(x) = 2x \ln x - ax$, where the tangent lines of functions $f(x)$ and $g(x)$ at $x = 1$ are parallel.

1. Find the equation of the tangent line of function $g(x)$ at point $(1, g(1))$;
2. Determine the range of values for the real number $a$ that makes $g(x) - f(x) \geq 0$ hold true for all $x > 0$.

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