
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
If both the dividend and divisor simultaneously equal zero, then the quotient, according to the above definition of division (see the previous question), can be any number \( m \), because \( m \cdot 0 = 0 \). However, it occurs that when both the dividend and divisor become zero simultaneously, the quotient has a definite value. For example, as \( x \rightarrow 0 \) the expression \( \frac{4x}{x} \), where both the numerator and denominator become zero, equals 4. Provide more interesting examples and explain more precisely the meaning of the word "become."

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