
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) = 2x^3 - ax^2 + 1, where a ∈ R.
(I) When a = 6, the line y = -6x + m is tangent to f(x). Find the value of m.
(II) If the function f(x) has exactly one zero in the interval (0, +∞), find the monotonic intervals of the function.
(III) When a > 0, if the sum of the maximum and minimum values of the function f(x) on the interval [-1, 1] is 1, find the value of the real number a.

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