
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
(x^2+1)(2x+1)^9=a_0+a_1(x+2)+a_2(x+2)^2+\ldots+a_{11}(x+2)^{11}, calculate the sum of the coefficients a_0 through a_11.

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