
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 $\left(x+2\right)^{9}=a_{0}+a_{1}x+a_{2}x^{2}+…+a_{9}x^{9}$, calculate the value of $\left(a_{1}+3a_{3}+5a_{5}+7a_{7}+9a_{9}\right)^{2}-\left(2a_{2}+4a_{4}+6a_{6}+8a_{8}\right)^{2}$.

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