
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
(1) Find the sum of the coefficients of the expanded form of the polynomial $(3x^4 - x^3 - 2x - 3)^{102}(3x - 5)^4(7x^3 - 5x - 1)^{67}$.  
(2) For the polynomial $x^{1000} - x(-x^3 - 2x^2 + 2)^{1000}$, what are the sums of the coefficients of the even and odd powers of $x$ in its expanded form?

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