
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
\begin{align*}
f(x+5)-f(x) &= 10x+25, \\
f(x^3-1) &= (f(x)-x)^3+x^3-3
\end{align*}
for all integers $x$. Find the ordered pair $(f(0), f(1))$.

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