
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 $f(x) = x^3 - ax^2$ ($a \in \mathbb{R}$).

(Ⅰ) If $f'(1) = 3$,

(i) Find the equation of the tangent line to the curve $y = f(x)$ at the point $(1, f(1))$,

(ii) Find the maximum value of $f(x)$ in the interval $[0, 2]$;

(Ⅱ) If $f(x) + x \geq 0$ always holds for $x \in [0, 2]$, find the range of the real number $a$.

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