
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^{2}+1)(2x+1)^{9}=a_{0}+a_{1}(x+2)+a_{2}(x+2)^{2}+\ldots+a_{n}(x+2)^{n}\\), then \\(a_{0}+a_{1}+a_{2}+\ldots+a_{n}=\\) \_\_\_\_\_\_.

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