
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 \\(f(x) = ax^3 - 6ax^2 + b\\) (where \\(a \neq 0\\)), and \\(x \in [-1, 2]\\), the maximum value of \\(f(x)\\) is \\(3\\), and the minimum value is \\(-29\\). Find the values of \\(a\\) and \\(b\\).

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