
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
Let $(3)_x^{-1}^{8} = (a)_8(x)^{8} + (a)_7(x)^{7} + \ldots + (a)_1(x) + (a)_0$, find:

(1) $a_8 + a_7 + \ldots + a_1$

(2) $(a)_8 + (a)_6 + (a)_4 + (a)_2 + (a)_0$

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