
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
Two students are studying fraction equivalency under variable transformations. They are specifically comparing the following two cases to determine if they are always equivalent:
- Case 1: \(\frac{x + a}{x + c}\) versus \(\frac{a}{c}\), for all x where c and x are nonzero.
- Case 2: \(\frac{b}{d}\) versus \(\frac{b}{d}\) when b and d are not equal to zero. Determine in which case the two fractions remain equivalent.
A) Case 1
B) Case 2
C) Both cases
D) Neither case

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