
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) = 2x³ + 3ax² + 1 (a ∈ R).
(I) Find the equation of the tangent line to f(x) at the point (1, f(1)) when a = 0.
(II) Determine the monotonic intervals of f(x).
(III) Find the minimum value of f(x) on the interval [0, 2].

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