
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
A function \( f: \mathbb{Z} \to \mathbb{Z} \) satisfies
\[
f(x+5) - f(x) = 10x + 25,
\]
\[
f(x^3 - 1) = (f(x) - x)^3 + x^3 - 3
\]
for all integers \( x \). Determine the ordered pair \( (f(0), f(1)) \).

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