
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 functions $f(x) = x \ln x$ and $g(x) = -x^2 + ax - 3$,
(1) Find the equation of the tangent line to the graph of $f(x)$ at the point $(1, 0)$;
(2) Find the minimum value of the function $f(x)$ on the interval $[t, t + \frac{1}{e}] (t > 0)$;
(3) Find the range of values of the real number $a$ such that $2f(x) \geq g(x)$ holds for all real numbers $x \in (0, +\infty)$.

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