
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
Why are the following approximations valid:

$$
\begin{aligned}
& 1.0023 \times 1.0057 \approx 1.008 \\
& 1.05 \times 9.97 \approx 10.02 \\
& 1.03 \times 0.99 \times 0.98 \approx 1 ?
\end{aligned}
$$

Provide general formulas that underlie these approximations and justify them. What is the approximation in each of these cases?

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