
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 $(x-3)^{3}(2x+1)^{5}=a_{0}+a_{1}x+a_{2}x^{2}+...+a_{8}x^{8}$, find the values of $a_{0}$ and $a_{0}+a_{2}+...+a_{8}$.

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