
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
In which of the expressions

$$
\left(1 + x^2 - x^3\right)^{1000} \quad \text{and} \quad \left(1 - x^2 + x^3\right)^{1000}
$$

will the coefficient for \( x^{20} \) be greater after expanding and combining like terms?

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