
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
Let $(x+1)^2+(x+1)^{11}=a+a_{1}(x+2)+a_{2}(x+2)^2+\ldots+a_{10}(x+2)^{10}+a_{11}(x+2)^{11}$. Find the value of $a_{10}$ (express your answer as a numerical value).

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