
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 the function $f(x) = x \ln x$,
(1) Find the equation of the tangent line to the curve $y = f(x)$ at the point $(1, f(1))$;
(2) If $f(x) \geq ax^2 + \frac{2}{a}$ ($a \neq 0$) holds true in the interval $(0, +\infty)$, find the minimum value of $a$.

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