
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 that $(x+2)^{8}=a_{0}+a_{1}(x+1)+a_{2}(x+1)^{2}+...a_{8}(x+1)^{8}$, where $a_{i}(i=0,1,2,...,8)$ are real constants, find the values of the following expressions (answer with numbers only):

(1) $a_{1}+a_{2}+...+a_{8}$;

(2) $a_{1}+a_{3}+a_{5}+a_{7}$

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