
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 $f(x)=x^3+3ax^2+3bx$ has an extremum at $x=2$, and its graph has a tangent line parallel to the line $6x+2y+5=0$ at $x=1$. Find the difference between the local maximum and minimum of $f(x)$.

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