
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 that $(x^2+1)^2(2x+1)^9 = a_0 + a_1(x+2) + a_2(x+2)^2 + \dots + a_{11}(x+2)^{11}$, find the value of $(a_0 + a_1 + a_2 + \dots + a_{11})$.

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