
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
Consider the expansion of \((x-2y)^{5}(x+3y)^{4}\) which can be expressed as \(a_{9}x^{9}+a_{8}x^{8}y+a_{7}x^{7}y^{2}+\ldots+a_{1}xy^{8}+a_{0}y^{9}\), find the value of \( a_{0} + a_{8} \).

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