
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
If $(x+2+m)^{9}=a_{0}+a_{1}(x+1)+a_{2}(x+1)^{2}+\ldots+a_{9}(x+1)^{9}$ and $(a_{0}+a_{2}+\ldots+a_{8})^{2}-(a_{1}+a_{3}+\ldots+a_{9})^{2}=3^{9}$, then the value of the real number $m$ is \_\_\_\_\_\_.

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