
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
On  $x-y$  plane,  let  $C: y=2006x^{3}-12070102x^{2}+\cdots.$  
Find the area of the region surrounded by the tangent line of  $C$  at  $x=2006$  and the curve  $C.$ 

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